Download 4 Trigonometry Partner Assignment

Name: ________________________ Class: ___________________ Date: __________
ID: A
Trigonometry Partner Assignment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Evaluate tan 4°, to four decimal places.
a. 1.6949
b. 0.9976
c. 0.6993
d. 0.0699
5. A school soccer field measures 45 m by 65 m. To
get home more quickly, you decide to walk along
the diagonal of the field. What is the angle of your
path, with respect to the 45-m side, to the nearest
degree?
a. 55°
b. 34°
c. 2°
d. 1°
2. In the triangle, BC = 12 cm and tan C = 0.583.
What is the length of the hypotenuse, to the nearest
tenth of a centimetre?
Use the diagram to answer the following
question(s).
a.
b.
c.
d.
14.2 cm
13.9 cm
7.0 cm
5.1 cm
6. Determine the length of x, to the nearest tenth of a
metre.
a. 5.7 m
b. 6.3 m
c. 7.0 m
d. 8.2 m
3. Evaluate tan 45°.
a. –1
b. 0
c. 1
d. undefined
7. Determine the length of y, to the nearest tenth of a
metre.
a. 5.7 m
b. 6.3 m
c. 7.0 m
d. 8.2 m
4. Determine the measure of ∠C, to the nearest
degree.
a.
b.
c.
d.
19°
20°
21°
22°
1
Name: ________________________
ID: A
11. Write the cosine ratio of ∠A.
8. Choose the correct formula for the cosine ratio of
∠A.
length of side opposite ∠A
a. cos A =
length of side adjacent to ∠A
length of hypotenuse
b. cos A =
length of side adjacent to ∠A
length of side opposite ∠A
c. cos A =
length of hypotenuse
length of side adjacent to ∠A
d. cos A =
length of hypotenuse
a.
b.
9. Determine the value of sin 28°, to four decimal
places.
a. 0.4695
b. 0.5317
c. 0.8829
d. 0.9709
c.
d.
12. In the triangle, AC = 26 cm and AB = 10 cm.
Determine the sine ratio of ∠A, to the nearest
thousandth.
10. In ABC, AC = 8 cm and BC = 11 cm. Determine
the sine ratio of ∠B, rounded to the nearest
thousandth.
a.
b.
c.
d.
AB
AC
BC
AB
AC
BC
BC
AC
a.
b.
c.
d.
0.588
0.728
0.809
1.375
2
0.385
0.417
0.923
1.833
Name: ________________________
ID: A
13. In ABC, BC = 48 cm and sin A = 0.96.
Determine the length of AC, to the nearest
centimetre.
a.
b.
c.
d.
Use the diagram to answer the following
question(s).
Kelly is flying a kite in a field. He lets out 40 m of
his kite string, which makes an angle of 72° with
the ground.
14 cm
24 cm
25 cm
50 cm
14. In the triangle, BC = 11 cm and cos B = 0.809.
Determine the length of AC, to the nearest
centimetre.
a.
b.
c.
d.
17. Determine the height of the kite above the ground,
to the nearest metre.
a. 12 m
b. 38 m
c. 42 m
d. 129 m
18. Suppose the sun is shining directly above the kite.
How far is the kite’s shadow from Kelly, to the
nearest metre?
a. 12 m
b. 38 m
c. 42 m
d. 129 m
8 cm
9 cm
10 cm
13 cm
15. Determine the value of cos 0°.
a. –1
b. 0
c. 1
d. undefined
19. An Airbus A320 aircraft is cruising at an altitude of
10 000 m. The aircraft is flying in a straight line
away from Monica, who is standing on the ground.
Monica observes that the angle of elevation of the
aircraft changes from 70° to 33° in one minute.
What is the cruising speed of the aircraft, to the
nearest kilometre per hour?
a. 463 km/h
b. 485 km/h
c. 665 km/h
d. 705 km/h
16. In TUV, UV = 8 m, ∠U = 90°, and ∠T = 38°.
Determine the measure of ∠V, to the nearest
degree
a. 42°
b. 52°
c. 90°
d. 128°
3
Name: ________________________
ID: A
8
.
11
ABC, to the nearest square
20. In the triangle, BC = 11 cm and tan B =
Determine the area of
centimetre.
a.
b.
c.
d.
121 cm2
88 cm2
64 cm2
44 cm2
Completion
Complete each statement.
1. The hypotenuse is the side
_________________________ the right angle in a
right triangle.
6. The angle between the horizontal and the line of
sight looking up to an object is called the angle of
_________________________ .
2. The tangent ratio of ∠A can be written as
_________________________ .
7. The angle of depression is the angle between the
horizontal and the line of sight looking
_________________________ to an object.
3. The sine ratio of ∠A compares the length of the
_________________________ side to the length of
the hypotenuse.
8. The _________________________ can be used to
determine the length of one side of a right triangle
given the lengths of the other two sides.
4. The cosine ratio of ∠A compares the length of the
_________________________ side to the length of
the hypotenuse.
9. In a right triangle, the
_________________________ side is the side that
forms one of the arms of the angle being
considered but is not the hypotenuse.
5. The angle of elevation is the angle between the
horizontal and the line of sight looking
_________________________ to an object.
10. The angle between the horizontal and the line of
sight looking down to an object is called the angle
of _________________________ .
4
Name: ________________________
ID: A
Matching
Match the correct side or angle of PQR to each of the following definitions, descriptions, or expressions. A term
may be used more than once or not at all.
a.
b.
c.
p
p
q
p
r
f.
q
r
g.
–1
h.
0
d.
Pythagorean theorem
i.
e.
q
j.
1
pq
2
1
1. the side opposite ∠Q
3. r 2 = q 2 + p 2
2. the side adjacent to ∠Q
4. sin Q
Match each term to the correct definition, description, or expression. A term may be used more than once or not
at all.
a. angle of elevation
e. Pythagorean theorem
b. angle of depression
f. sine ratio
c. cosine ratio
g. tangent ratio
d. hypotenuse
h. trigonometry
length of side opposite an acute angle
length of side adjacent to an acute angle
5. in a right triangle with side lengths a, b, and c,
where c is the hypotenuse, a 2 + b 2 = c 2
8.
6. the study of angles and triangles
9. the side opposite the right angle in a right triangle
7.
length of side opposite an acute angle
length of hypotenuse
10.
5
length of side adjacent to an acute angle
length of hypotenuse
Name: ________________________
ID: A
Short Answer
1. Juanita is helping build a wheelchair ramp at her
community centre. The ramp must reach a vertical
distance of 1.5 m. If the ramp must make an angle
of 6° with the ground, how long will the ramp be?
Answer to the nearest tenth of a metre.
3. In right triangle ABC, the hypotenuse, AB, is 15
cm and ∠B is 25°. How long is AC, to the nearest
centimetre?
2. A telephone pole is secured with a guy wire as
shown in the diagram. The guy wire makes an
angle of 75° with the ground and is secured to the
ground 6 m from the bottom of the pole. Determine
the height of the telephone pole, to the nearest tenth
of a metre.
4. In XYZ, XY and XZ have equal lengths of 6 cm.
YZ is 10 cm. Determine the measure of ∠X, to the
nearest degree.
5. In the diagram, label the hypotenuse, the opposite
side, and the adjacent side relative to ∠C.
Problem
1. The percent grade of a road is the ratio of the
vertical rise of the road to the horizontal distance,
expressed as a percent. A road in the mountains has
a vertical rise of 40 m over 1 km of horizontal
distance.
a) Determine the percent grade of the road, to the
nearest percent.
b) What is the angle of elevation of the road, to the
nearest degree?
2. Myriam is participating in a water-skiing
competition. She goes over a water-ski ramp that is
4.0 m long. When she leaves the ramp, she is 1.7 m
above the surface of the water.
a) What is the horizontal length of the ramp along
the surface of the water, to the nearest tenth of a
metre?
b) Determine the angle of elevation of the ramp, to
the nearest degree.
6
ID: A
Trigonometry Partner Assignment
Answer Section
MULTIPLE CHOICE
1. ANS:
NAT:
2. ANS:
NAT:
KEY:
3. ANS:
NAT:
4. ANS:
NAT:
KEY:
5. ANS:
NAT:
KEY:
6. ANS:
NAT:
KEY:
7. ANS:
NAT:
KEY:
8. ANS:
NAT:
9. ANS:
NAT:
10. ANS:
NAT:
KEY:
11. ANS:
NAT:
KEY:
12. ANS:
NAT:
KEY:
13. ANS:
NAT:
KEY:
14. ANS:
NAT:
KEY:
15. ANS:
NAT:
16. ANS:
NAT:
D
PTS: 1
DIF: B
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
KEY: tangent ratio | calculate a tangent ratio
B
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry | Pythagorean theorem | hypotenuse | right triangle
C
PTS: 1
DIF: A
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
KEY: tangent ratio | calculate a tangent ratio
C
PTS: 1
DIF: B
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine an angle measure | right triangle
A
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
tangent ratio | determine an angle measure
C
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry
B
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry
D
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: cosine ratio | define the cosine ratio
A
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | calculate a sine ratio
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | calculate a sine ratio | right triangle
A
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
cosine ratio | write a cosine ratio | right triangle
C
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | calculate a sine ratio | right triangle
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | determine a distance using trigonometry | right triangle
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
cosine ratio | determine a distance using trigonometry | right triangle
C
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: cosine ratio | calculate a cosine ratio
B
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | determine an angle measure
1
ID: A
17. ANS:
NAT:
KEY:
18. ANS:
NAT:
KEY:
19. ANS:
NAT:
20. ANS:
NAT:
B
PTS: 1
DIF: B
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
sine ratio | determine a distance using trigonometry | solve a right triangle
A
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
cosine ratio | determine a distance using trigonometry | solve a right triangle
D
PTS: 1
DIF: D
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
KEY: sine ratio | solve a right triangle
D
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
KEY: tangent ratio | right triangle | area
COMPLETION
1. ANS: opposite
PTS: 1
DIF: A
TOP: The Tangent Ratio
2. ANS:
Example:
length of side opposite ∠A
tanA =
length of side adjacent to ∠A
OBJ: Section 3.1 NAT: M4
KEY: right triangle | hypotenuse
PTS:
TOP:
KEY:
3. ANS:
1
DIF: B
OBJ: Section 3.1 NAT: M4
The Tangent Ratio
tangent ratio | write a tangent ratio | primary trigonometric ratios
opposite
PTS:
TOP:
KEY:
4. ANS:
1
DIF: A
OBJ: Section 3.2 NAT: M4
The Sine and Cosine Ratios
sine ratio | define the sine ratio | opposite side | primary trigonometric ratios
adjacent
PTS:
TOP:
KEY:
5. ANS:
1
DIF: A
OBJ: Section 3.2 NAT: M4
The Sine and Cosine Ratios
cosine ratio | define the cosine ratio | adjacent side | primary trigonometric ratios
up
PTS: 1
DIF: A
TOP: Solving Right Triangles
6. ANS: elevation
OBJ: Section 3.3 NAT: M4
KEY: angle of elevation
PTS: 1
DIF: B
TOP: Solving Right Triangles
7. ANS: down
OBJ: Section 3.3 NAT: M4
KEY: angle of elevation
PTS: 1
DIF: A
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: angle of depression
2
ID: A
8. ANS: Pythagorean theorem
PTS: 1
DIF: A
TOP: Solving Right Triangles
9. ANS: adjacent
OBJ: Section 3.3 NAT: M4
KEY: Pythagorean theorem
PTS: 1
DIF: B
TOP: The Sine and Cosine Ratios
10. ANS: depression
OBJ: Section 3.2 NAT: M4
KEY: adjacent side
PTS: 1
DIF: A
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: angle of depression
MATCHING
1. ANS:
NAT:
2. ANS:
NAT:
3. ANS:
NAT:
4. ANS:
NAT:
5. ANS:
NAT:
6. ANS:
NAT:
7. ANS:
NAT:
8. ANS:
NAT:
KEY:
9. ANS:
NAT:
10. ANS:
NAT:
KEY:
E
M4
A
M4
D
M4
F
M4
PTS:
TOP:
PTS:
TOP:
PTS:
TOP:
PTS:
TOP:
1
DIF: A
The Tangent Ratio
1
DIF: A
The Tangent Ratio
1
DIF: A
The Tangent Ratio
1
DIF: B
The Sine and Cosine Ratios
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
Section 3.1
label a right triangle | opposite side
Section 3.1
label a right triangle | adjacent side
Section 3.1
Pythagorean theorem
Section 3.2
sine ratio | primary trigonometric ratios
E
PTS: 1
DIF: A
M4
TOP: Solving Right Triangles
H
PTS: 1
DIF: A
M4
TOP: The Tangent Ratio
F
PTS: 1
DIF: B
M4
TOP: The Sine and Cosine Ratios
G
PTS: 1
DIF: B
M4
TOP: The Tangent Ratio
tangent ratio | primary trigonometric ratios
D
PTS: 1
DIF: A
M4
TOP: The Tangent Ratio
C
PTS: 1
DIF: B
M4
TOP: The Sine and Cosine Ratios
cosine ratio | primary trigonometric ratios
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
OBJ:
Section 3.3
Pythagorean theorem
Section 3.1
trigonometry
Section 3.2
sine ratio | primary trigonometric ratios
Section 3.1
3
OBJ: Section 3.1
KEY: hypotenuse
OBJ: Section 3.2
ID: A
SHORT ANSWER
1. ANS:
Let x represent the length of the ramp, in metres.
vertical height of ramp
sin6° =
length of ramp
sin6° =
x=
1.5
x
1.5
sin6°
x = 14.3502. . .
The wheelchair ramp must be approximately 14.4 m long.
PTS: 1
DIF: B
OBJ: Section 3.1 NAT: M4
TOP: The Tangent Ratio
KEY: sine ratio | determine a distance using trigonometry
2. ANS:
Let h represent the height of the pole, in metres.
height of pole
tan75° =
distance of wire from base
tan75° =
h
6
22.3923. . . = h
The pole is approximately 22.4 m tall.
PTS: 1
DIF: B
OBJ: Section 3.1 NAT: M4
TOP: The Tangent Ratio
KEY: tangent ratio | determine a distance using trigonometry | right triangle
3. ANS:
side opposite ∠B
sin B =
hypotenuse
sin 25° =
AC
15
15(sin 25°) = AC
6.3393. . . = AC
AC is approximately 6 cm long.
PTS: 1
DIF: B
OBJ: Section 3.2 NAT: M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | determine a distance using trigonometry | right triangle
4
ID: A
4. ANS:
cos Z =
side adjacent to ∠Z
hypotenuse
cos Z =
ZW
XZ
cos Z =
5
6
cos Z = 0.8333
Z = cos −1(0.8333)
Z = 33.5573. . .
∠Z measures approximately 34°. ∠Y is equal to ∠Z.
180 = ∠X + ∠Y + ∠Z
180 = ∠X + 34 + 34
180 = ∠X + 68
112 = ∠X
∠X measures approximately 112°.
PTS: 1
DIF: C
TOP: The Sine and Cosine Ratios
5. ANS:
PTS: 1
DIF:
TOP: The Tangent Ratio
A
OBJ: Section 3.2 NAT: M4
KEY: cosine ratio | determine an angle measure | isosceles triangle
OBJ: Section 3.1 NAT: M4
KEY: primary trigonometric ratios | label a right triangle
5
ID: A
PROBLEM
1. ANS:
a)
1 km = 1000 m
ÊÁ
ˆ˜
vertical rise
˜˜ × 100
percent grade = ÁÁÁ
ÁË horizontal distance ˜˜¯
ÁÊ 40 ˜ˆ˜
˜˜ × 100
percent grade = ÁÁÁÁ
˜
Ë 1000 ¯
percent grade = 0.04 × 100
percent grade = 4
The percent grade of the road is 4%.
b) Let θ represent the angle of elevation, in degrees.
vertical rise
tan θ =
horizontal distance
tan θ =
40
1000
θ = tan−1 (0.04)
θ = 2.2906. . .
The angle of elevation of the road is approximately 2°.
PTS: 1
DIF: D
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: tangent ratio | angle of elevation
6
ID: A
2. ANS:
a) Let x represent the length of the ramp along the surface of the water, in metres.
Draw a diagram of the situation.
x 2 + 1.7 2 = 4.0 2
x 2 = 16 − 2.89
x 2 = 13.11
x ≈ 3.62
The horizontal length of the ramp along the surface of the water is about 3.6 m.
b) sinθ =
1.7
4.0
sinθ = 0.425
θ = 25.1507. . .
θ ≈ 25
The angle of elevation of the ramp is about 25°.
PTS: 1
DIF: B
TOP: The Sine and Cosine Ratios
OBJ: Section 3.2 NAT: M4
KEY: sine ratio | angle of elevation | Pythagorean theorem
7
Name: ________________________ Class: ___________________ Date: __________
ID: A
Trigonometry Partner Assignment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Evaluate tan 4°, to four decimal places.
a. 1.6949
b. 0.9976
c. 0.6993
d. 0.0699
5. A school soccer field measures 45 m by 65 m. To
get home more quickly, you decide to walk along
the diagonal of the field. What is the angle of your
path, with respect to the 45-m side, to the nearest
degree?
a. 55°
b. 34°
c. 2°
d. 1°
2. In the triangle, BC = 12 cm and tan C = 0.583.
What is the length of the hypotenuse, to the nearest
tenth of a centimetre?
Use the diagram to answer the following
question(s).
a.
b.
c.
d.
14.2 cm
13.9 cm
7.0 cm
5.1 cm
6. Determine the length of x, to the nearest tenth of a
metre.
a. 5.7 m
b. 6.3 m
c. 7.0 m
d. 8.2 m
3. Evaluate tan 45°.
a. –1
b. 0
c. 1
d. undefined
7. Determine the length of y, to the nearest tenth of a
metre.
a. 5.7 m
b. 6.3 m
c. 7.0 m
d. 8.2 m
4. Determine the measure of ∠C, to the nearest
degree.
a.
b.
c.
d.
19°
20°
21°
22°
1
Name: ________________________
ID: A
11. Write the cosine ratio of ∠A.
8. Choose the correct formula for the cosine ratio of
∠A.
length of side opposite ∠A
a. cos A =
length of side adjacent to ∠A
length of hypotenuse
b. cos A =
length of side adjacent to ∠A
length of side opposite ∠A
c. cos A =
length of hypotenuse
length of side adjacent to ∠A
d. cos A =
length of hypotenuse
a.
b.
9. Determine the value of sin 28°, to four decimal
places.
a. 0.4695
b. 0.5317
c. 0.8829
d. 0.9709
c.
d.
12. In the triangle, AC = 26 cm and AB = 10 cm.
Determine the sine ratio of ∠A, to the nearest
thousandth.
10. In ABC, AC = 8 cm and BC = 11 cm. Determine
the sine ratio of ∠B, rounded to the nearest
thousandth.
a.
b.
c.
d.
AB
AC
BC
AB
AC
BC
BC
AC
a.
b.
c.
d.
0.588
0.728
0.809
1.375
2
0.385
0.417
0.923
1.833
Name: ________________________
ID: A
13. In ABC, BC = 48 cm and sin A = 0.96.
Determine the length of AC, to the nearest
centimetre.
a.
b.
c.
d.
Use the diagram to answer the following
question(s).
Kelly is flying a kite in a field. He lets out 40 m of
his kite string, which makes an angle of 72° with
the ground.
14 cm
24 cm
25 cm
50 cm
14. In the triangle, BC = 11 cm and cos B = 0.809.
Determine the length of AC, to the nearest
centimetre.
a.
b.
c.
d.
17. Determine the height of the kite above the ground,
to the nearest metre.
a. 12 m
b. 38 m
c. 42 m
d. 129 m
18. Suppose the sun is shining directly above the kite.
How far is the kite’s shadow from Kelly, to the
nearest metre?
a. 12 m
b. 38 m
c. 42 m
d. 129 m
8 cm
9 cm
10 cm
13 cm
15. Determine the value of cos 0°.
a. –1
b. 0
c. 1
d. undefined
19. An Airbus A320 aircraft is cruising at an altitude of
10 000 m. The aircraft is flying in a straight line
away from Monica, who is standing on the ground.
Monica observes that the angle of elevation of the
aircraft changes from 70° to 33° in one minute.
What is the cruising speed of the aircraft, to the
nearest kilometre per hour?
a. 463 km/h
b. 485 km/h
c. 665 km/h
d. 705 km/h
16. In TUV, UV = 8 m, ∠U = 90°, and ∠T = 38°.
Determine the measure of ∠V, to the nearest
degree
a. 42°
b. 52°
c. 90°
d. 128°
3
Name: ________________________
ID: A
8
.
11
ABC, to the nearest square
20. In the triangle, BC = 11 cm and tan B =
Determine the area of
centimetre.
a.
b.
c.
d.
121 cm2
88 cm2
64 cm2
44 cm2
Completion
Complete each statement.
1. The hypotenuse is the side
_________________________ the right angle in a
right triangle.
6. The angle between the horizontal and the line of
sight looking up to an object is called the angle of
_________________________ .
2. The tangent ratio of ∠A can be written as
_________________________ .
7. The angle of depression is the angle between the
horizontal and the line of sight looking
_________________________ to an object.
3. The sine ratio of ∠A compares the length of the
_________________________ side to the length of
the hypotenuse.
8. The _________________________ can be used to
determine the length of one side of a right triangle
given the lengths of the other two sides.
4. The cosine ratio of ∠A compares the length of the
_________________________ side to the length of
the hypotenuse.
9. In a right triangle, the
_________________________ side is the side that
forms one of the arms of the angle being
considered but is not the hypotenuse.
5. The angle of elevation is the angle between the
horizontal and the line of sight looking
_________________________ to an object.
10. The angle between the horizontal and the line of
sight looking down to an object is called the angle
of _________________________ .
4
Name: ________________________
ID: A
Matching
Match the correct side or angle of PQR to each of the following definitions, descriptions, or expressions. A term
may be used more than once or not at all.
a.
b.
c.
p
p
q
p
r
f.
q
r
g.
–1
h.
0
d.
Pythagorean theorem
i.
e.
q
j.
1
pq
2
1
1. the side opposite ∠Q
3. r 2 = q 2 + p 2
2. the side adjacent to ∠Q
4. sin Q
Match each term to the correct definition, description, or expression. A term may be used more than once or not
at all.
a. angle of elevation
e. Pythagorean theorem
b. angle of depression
f. sine ratio
c. cosine ratio
g. tangent ratio
d. hypotenuse
h. trigonometry
length of side opposite an acute angle
length of side adjacent to an acute angle
5. in a right triangle with side lengths a, b, and c,
where c is the hypotenuse, a 2 + b 2 = c 2
8.
6. the study of angles and triangles
9. the side opposite the right angle in a right triangle
7.
length of side opposite an acute angle
length of hypotenuse
10.
5
length of side adjacent to an acute angle
length of hypotenuse
Name: ________________________
ID: A
Short Answer
1. Juanita is helping build a wheelchair ramp at her
community centre. The ramp must reach a vertical
distance of 1.5 m. If the ramp must make an angle
of 6° with the ground, how long will the ramp be?
Answer to the nearest tenth of a metre.
3. In right triangle ABC, the hypotenuse, AB, is 15
cm and ∠B is 25°. How long is AC, to the nearest
centimetre?
2. A telephone pole is secured with a guy wire as
shown in the diagram. The guy wire makes an
angle of 75° with the ground and is secured to the
ground 6 m from the bottom of the pole. Determine
the height of the telephone pole, to the nearest tenth
of a metre.
4. In XYZ, XY and XZ have equal lengths of 6 cm.
YZ is 10 cm. Determine the measure of ∠X, to the
nearest degree.
5. In the diagram, label the hypotenuse, the opposite
side, and the adjacent side relative to ∠C.
Problem
1. The percent grade of a road is the ratio of the
vertical rise of the road to the horizontal distance,
expressed as a percent. A road in the mountains has
a vertical rise of 40 m over 1 km of horizontal
distance.
a) Determine the percent grade of the road, to the
nearest percent.
b) What is the angle of elevation of the road, to the
nearest degree?
2. Myriam is participating in a water-skiing
competition. She goes over a water-ski ramp that is
4.0 m long. When she leaves the ramp, she is 1.7 m
above the surface of the water.
a) What is the horizontal length of the ramp along
the surface of the water, to the nearest tenth of a
metre?
b) Determine the angle of elevation of the ramp, to
the nearest degree.
6
ID: A
Trigonometry Partner Assignment
Answer Section
MULTIPLE CHOICE
1. ANS:
NAT:
2. ANS:
NAT:
KEY:
3. ANS:
NAT:
4. ANS:
NAT:
KEY:
5. ANS:
NAT:
KEY:
6. ANS:
NAT:
KEY:
7. ANS:
NAT:
KEY:
8. ANS:
NAT:
9. ANS:
NAT:
10. ANS:
NAT:
KEY:
11. ANS:
NAT:
KEY:
12. ANS:
NAT:
KEY:
13. ANS:
NAT:
KEY:
14. ANS:
NAT:
KEY:
15. ANS:
NAT:
16. ANS:
NAT:
D
PTS: 1
DIF: B
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
KEY: tangent ratio | calculate a tangent ratio
B
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry | Pythagorean theorem | hypotenuse | right triangle
C
PTS: 1
DIF: A
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
KEY: tangent ratio | calculate a tangent ratio
C
PTS: 1
DIF: B
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine an angle measure | right triangle
A
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
tangent ratio | determine an angle measure
C
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry
B
PTS: 1
DIF: C
OBJ: Section 3.1
M4
TOP: The Tangent Ratio
tangent ratio | determine a distance using trigonometry
D
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: cosine ratio | define the cosine ratio
A
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | calculate a sine ratio
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | calculate a sine ratio | right triangle
A
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
cosine ratio | write a cosine ratio | right triangle
C
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | calculate a sine ratio | right triangle
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
sine ratio | determine a distance using trigonometry | right triangle
A
PTS: 1
DIF: B
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
cosine ratio | determine a distance using trigonometry | right triangle
C
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: cosine ratio | calculate a cosine ratio
B
PTS: 1
DIF: A
OBJ: Section 3.2
M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | determine an angle measure
1
ID: A
17. ANS:
NAT:
KEY:
18. ANS:
NAT:
KEY:
19. ANS:
NAT:
20. ANS:
NAT:
B
PTS: 1
DIF: B
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
sine ratio | determine a distance using trigonometry | solve a right triangle
A
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
cosine ratio | determine a distance using trigonometry | solve a right triangle
D
PTS: 1
DIF: D
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
KEY: sine ratio | solve a right triangle
D
PTS: 1
DIF: C
OBJ: Section 3.3
M4
TOP: Solving Right Triangles
KEY: tangent ratio | right triangle | area
COMPLETION
1. ANS: opposite
PTS: 1
DIF: A
TOP: The Tangent Ratio
2. ANS:
Example:
length of side opposite ∠A
tanA =
length of side adjacent to ∠A
OBJ: Section 3.1 NAT: M4
KEY: right triangle | hypotenuse
PTS:
TOP:
KEY:
3. ANS:
1
DIF: B
OBJ: Section 3.1 NAT: M4
The Tangent Ratio
tangent ratio | write a tangent ratio | primary trigonometric ratios
opposite
PTS:
TOP:
KEY:
4. ANS:
1
DIF: A
OBJ: Section 3.2 NAT: M4
The Sine and Cosine Ratios
sine ratio | define the sine ratio | opposite side | primary trigonometric ratios
adjacent
PTS:
TOP:
KEY:
5. ANS:
1
DIF: A
OBJ: Section 3.2 NAT: M4
The Sine and Cosine Ratios
cosine ratio | define the cosine ratio | adjacent side | primary trigonometric ratios
up
PTS: 1
DIF: A
TOP: Solving Right Triangles
6. ANS: elevation
OBJ: Section 3.3 NAT: M4
KEY: angle of elevation
PTS: 1
DIF: B
TOP: Solving Right Triangles
7. ANS: down
OBJ: Section 3.3 NAT: M4
KEY: angle of elevation
PTS: 1
DIF: A
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: angle of depression
2
ID: A
8. ANS: Pythagorean theorem
PTS: 1
DIF: A
TOP: Solving Right Triangles
9. ANS: adjacent
OBJ: Section 3.3 NAT: M4
KEY: Pythagorean theorem
PTS: 1
DIF: B
TOP: The Sine and Cosine Ratios
10. ANS: depression
OBJ: Section 3.2 NAT: M4
KEY: adjacent side
PTS: 1
DIF: A
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: angle of depression
MATCHING
1. ANS:
NAT:
2. ANS:
NAT:
3. ANS:
NAT:
4. ANS:
NAT:
5. ANS:
NAT:
6. ANS:
NAT:
7. ANS:
NAT:
8. ANS:
NAT:
KEY:
9. ANS:
NAT:
10. ANS:
NAT:
KEY:
E
M4
A
M4
D
M4
F
M4
PTS:
TOP:
PTS:
TOP:
PTS:
TOP:
PTS:
TOP:
1
DIF: A
The Tangent Ratio
1
DIF: A
The Tangent Ratio
1
DIF: A
The Tangent Ratio
1
DIF: B
The Sine and Cosine Ratios
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
Section 3.1
label a right triangle | opposite side
Section 3.1
label a right triangle | adjacent side
Section 3.1
Pythagorean theorem
Section 3.2
sine ratio | primary trigonometric ratios
E
PTS: 1
DIF: A
M4
TOP: Solving Right Triangles
H
PTS: 1
DIF: A
M4
TOP: The Tangent Ratio
F
PTS: 1
DIF: B
M4
TOP: The Sine and Cosine Ratios
G
PTS: 1
DIF: B
M4
TOP: The Tangent Ratio
tangent ratio | primary trigonometric ratios
D
PTS: 1
DIF: A
M4
TOP: The Tangent Ratio
C
PTS: 1
DIF: B
M4
TOP: The Sine and Cosine Ratios
cosine ratio | primary trigonometric ratios
OBJ:
KEY:
OBJ:
KEY:
OBJ:
KEY:
OBJ:
Section 3.3
Pythagorean theorem
Section 3.1
trigonometry
Section 3.2
sine ratio | primary trigonometric ratios
Section 3.1
3
OBJ: Section 3.1
KEY: hypotenuse
OBJ: Section 3.2
ID: A
SHORT ANSWER
1. ANS:
Let x represent the length of the ramp, in metres.
vertical height of ramp
sin6° =
length of ramp
sin6° =
x=
1.5
x
1.5
sin6°
x = 14.3502. . .
The wheelchair ramp must be approximately 14.4 m long.
PTS: 1
DIF: B
OBJ: Section 3.1 NAT: M4
TOP: The Tangent Ratio
KEY: sine ratio | determine a distance using trigonometry
2. ANS:
Let h represent the height of the pole, in metres.
height of pole
tan75° =
distance of wire from base
tan75° =
h
6
22.3923. . . = h
The pole is approximately 22.4 m tall.
PTS: 1
DIF: B
OBJ: Section 3.1 NAT: M4
TOP: The Tangent Ratio
KEY: tangent ratio | determine a distance using trigonometry | right triangle
3. ANS:
side opposite ∠B
sin B =
hypotenuse
sin 25° =
AC
15
15(sin 25°) = AC
6.3393. . . = AC
AC is approximately 6 cm long.
PTS: 1
DIF: B
OBJ: Section 3.2 NAT: M4
TOP: The Sine and Cosine Ratios
KEY: sine ratio | determine a distance using trigonometry | right triangle
4
ID: A
4. ANS:
cos Z =
side adjacent to ∠Z
hypotenuse
cos Z =
ZW
XZ
cos Z =
5
6
cos Z = 0.8333
Z = cos −1(0.8333)
Z = 33.5573. . .
∠Z measures approximately 34°. ∠Y is equal to ∠Z.
180 = ∠X + ∠Y + ∠Z
180 = ∠X + 34 + 34
180 = ∠X + 68
112 = ∠X
∠X measures approximately 112°.
PTS: 1
DIF: C
TOP: The Sine and Cosine Ratios
5. ANS:
PTS: 1
DIF:
TOP: The Tangent Ratio
A
OBJ: Section 3.2 NAT: M4
KEY: cosine ratio | determine an angle measure | isosceles triangle
OBJ: Section 3.1 NAT: M4
KEY: primary trigonometric ratios | label a right triangle
5
ID: A
PROBLEM
1. ANS:
a)
1 km = 1000 m
ÊÁ
ˆ˜
vertical rise
˜˜ × 100
percent grade = ÁÁÁ
ÁË horizontal distance ˜˜¯
ÁÊ 40 ˜ˆ˜
˜˜ × 100
percent grade = ÁÁÁÁ
˜
Ë 1000 ¯
percent grade = 0.04 × 100
percent grade = 4
The percent grade of the road is 4%.
b) Let θ represent the angle of elevation, in degrees.
vertical rise
tan θ =
horizontal distance
tan θ =
40
1000
θ = tan−1 (0.04)
θ = 2.2906. . .
The angle of elevation of the road is approximately 2°.
PTS: 1
DIF: D
TOP: Solving Right Triangles
OBJ: Section 3.3 NAT: M4
KEY: tangent ratio | angle of elevation
6
ID: A
2. ANS:
a) Let x represent the length of the ramp along the surface of the water, in metres.
Draw a diagram of the situation.
x 2 + 1.7 2 = 4.0 2
x 2 = 16 − 2.89
x 2 = 13.11
x ≈ 3.62
The horizontal length of the ramp along the surface of the water is about 3.6 m.
b) sinθ =
1.7
4.0
sinθ = 0.425
θ = 25.1507. . .
θ ≈ 25
The angle of elevation of the ramp is about 25°.
PTS: 1
DIF: B
TOP: The Sine and Cosine Ratios
OBJ: Section 3.2 NAT: M4
KEY: sine ratio | angle of elevation | Pythagorean theorem
7