Download Unit 2 - Review for Final Exam

Unit 2 - Review for Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine tan A and tan C.
C
4
A
6
B
a. tan A = 1.5; tan C = 0.6
b. tan A = 0.6; tan C = 0.8321...
____
c. tan A = 0.6; tan C = 1.5
d. tan A = 0.5547...; tan C = 1.5
2. Determine the measure of D to the nearest tenth of a degree.
13
D
E
7
F
a. 28.3°
____
b. 32.6°
c. 57.4°
d. 61.7°
3. Determine the angle of inclination of the line to the nearest tenth of a degree.
|
4.1
|
9.7
a. 65.0°
b. 22.9°
c. 67.1°
d. 25.0°
____
4. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 19%.
a. 79.0°
b. 79.2°
c. 10.8°
d. 11.0°
____
5. Determine the measure of ABD to the nearest tenth of a degree.
C
D
|
|
8 cm
19 cm
A
a. 65.1°
B
b. 67.2°
c. 22.8°
d. 24.9°
____
6. A ladder leans against the side of a building. The top of the ladder is 4.5 m from the ground. The base of the
ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground?
a. 77°
b. 13°
c. 10°
d. 82°
____
7. Determine the tangent ratio for K.
L
M
20
101
K
a.
____
b.
20
99
20
101
c.
101
20
d.
99
20
8. Determine the length of side z to the nearest tenth of a centimetre.
X
3.8 cm
z
65°
Z
Y
a. 9.0 cm
____
b. 1.8 cm
c. 4.2 cm
d. 8.1 cm
9. Determine the length of side l to the nearest tenth of a metre.
L
16.1 m
M
l
57°
N
a. 10.5 m
b. 24.8 m
c. 13.5 m
d. 8.8 m
____ 10. A guy wire is attached to a tower at a point that is 5.5 m above the ground. The angle between the wire and
the level ground is 56. How far from the base of the tower is the wire anchored to the ground, to the nearest
tenth of a metre?
a. 3.1 m
b. 6.6 m
c. 3.7 m
d. 8.2 m
____ 11. A ladder leans against a wall. The base of the ladder is on level ground 1.2 m from the wall. The angle
between the ladder and the ground is 70. How far up the wall does the ladder reach, to the nearest tenth of a
metre?
a. 0.4 m
b. 1.3 m
c. 3.5 m
d. 3.3 m
____ 12. A road has an angle of inclination of 16. Determine the increase in altitude of the road, to the nearest metre,
for every 175 m of horizontal distance.
a. 610 m
b. 168 m
c. 50 m
d. 48 m
____ 13. A flagpole casts a shadow that is 21 m long when the angle between the sun’s rays and the ground is 48.
Determine the height of the flagpole, to the nearest metre.
a. 19 m
b. 16 m
c. 14 m
d. 23 m
____ 14. A surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the base of a tower. The angle
between the horizontal and the line of sight to the top of the tower was 21. Determine the height of the tower
to the nearest tenth of a metre.
a. 157.8 m
b. 23.0 m
c. 24.5 m
d. 65.8 m
____ 15. From a point 18 ft. from the base of a flagpole, Seema used a clinometer to sight the top of the flagpole.
Seema held the clinometer 5 ft. 3 in. above the ground. The angle between the horizontal and the line of sight
was 52. Determine the height of the flagpole to the nearest foot.
a. 28 ft.
b. 34 ft.
c. 19 ft.
d. 23 ft.
____ 16. Determine sin G and cos G to the nearest hundredth.
40
F
E
9
41
G
a. sin G = 0.98; cos G = 4.56
b. sin G = 0.22; cos G = 0.98
c. sin G = 1.03; cos G = 0.22
d. sin G = 0.98; cos G = 0.22
____ 17. Determine the measure of D to the nearest tenth of a degree.
D
E
10
23
F
a. 64.2°
b. 66.5°
c. 25.8°
d. 23.5°
____ 18. Determine the measure of Q to the nearest tenth of a degree.
P
13
Q
25
R
a. 58.7°
b. 62.5°
c. 31.3°
d. 27.5°
____ 19. A helicopter is hovering 350 m above a road. A car stopped on the side of the road is 450 m from the
helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree?
a. 52°
b. 39°
c. 51°
d. 38°
____ 20. A ladder is 11.0 m long. It leans against a wall. The base of the ladder is 3.3 m from the wall. What is the
angle of inclination of the ladder to the nearest tenth of a degree?
a. 72.5
b. 17.5
c. 73.3
d. 16.7
____ 21. A rope that anchors a hot air balloon to the ground is 136 m long. The balloon is 72 m above the ground.
What is the angle of inclination of the rope to the nearest tenth of a degree?
a. 58.0
b. 62.1
c. 32.0
d. 27.9
____ 22. Determine the length of MN to the nearest tenth of an centimetre.
L
M
15.8 cm
51°
N
a. 19.5 cm
b. 25.1 cm
c. 9.9 cm
____ 23. Determine the length of XY to the nearest tenth of a centimetre.
Y
X
20.1 cm
59°
Z
d. 12.3 cm
a. 10.4 cm
b. 17.2 cm
c. 33.5 cm
d. 23.4 cm
____ 24. Determine the length of RS to the nearest tenth of a metre.
R
29°
18.8 m
T
a. 21.5 m
S
b. 10.4 m
c. 16.4 m
d. 38.8 m
____ 25. Determine the length of DE to the nearest tenth of a centimetre.
D
11.3 cm
E
32°
a. 13.3 cm
F
b. 21.3 cm
c. 6.0 cm
d. 18.1 cm
____ 26. From the start of a runway, the angle of elevation of an approaching airplane is 17.5. At this time, the plane
is flying at an altitude of 6.2 km. How far is the plane from the start of the runway to the nearest tenth of a
kilometre?
a. 6.5 km
b. 1.9 km
c. 20.6 km
d. 19.7 km
____ 27. A surveyor made the measurements shown in the diagram. Determine the distance from R to S, to the nearest
hundredth of a metre.
Q
S
38.91 m
56.5°
R
a. 46.66 m
b. 70.50 m
c. 25.75 m
d. 58.79 m
____ 28. A ladder is 8.0 m long. It leans against a wall. The angle of inclination of the ladder is 72. To the nearest
tenth of a metre, how far from the wall is the base of the ladder?
a. 2.6 m
b. 7.6 m
c. 25.9 m
d. 2.5 m
____ 29. A guy wire is attached to a tower at a point that is 7.5 m above the ground. The angle of inclination of the
wire is 67. Determine the length of the wire to the nearest tenth of a metre.
a. 18.7 m
b. 20.2 m
c. 8.1 m
d. 7.9 m
____ 30. Solve this right triangle. Give the measures to the nearest tenth.
U
6.5.0 cm
V
13.0 cm
W
a.
b.
cm c.
cm d.
cm
cm
____ 31. Solve this right triangle. Give the measures to the nearest tenth.
F
8.0 m
23°
G
H
a.
b.
m
m
c.
d.
m
m
____ 32. The front of a tent has the shape of an isosceles triangle with equal sides 177 cm long. The measure of the
angle at the peak of the tent is 105. Calculate the maximum headroom in the tent to the nearest centimetre.
105°
177 cm
177 cm
a. 140 cm
b. 136 cm
c. 108 cm
d. 250 cm
____ 33. Determine the perimeter of an equilateral triangle with height 9.8 cm. Give the measure to the nearest tenth of
a centimetre.
a. 55.4 cm
b. 33.9 cm
c. 25.5 cm
____ 34. Determine the length of RS to the nearest tenth of a centimetre.
d. 58.8 cm
R
5.7 cm
Q
54°
S
41°
T
a.
cm
b.
cm
c.
cm
d.
cm
d.
cm
____ 35. Determine the length of MN to the nearest tenth of a centimetre.
K
L
53°
M
8.9 cm
35°
N
a.
cm
b.
cm
c.
cm
____ 36. Two trees are 60 yd. apart. From a point halfway between the trees, the angles of elevation of the tops of the
trees are measured. What is the height of each tree to the nearest yard?
tree
tree
36°
31°
60 yd.
a. 37 yd.; 35 yd.
b. 22 yd.; 18 yd.
c. 41 yd.; 50 yd.
d. 41 yd.; 49 yd.
____ 37. From the top of an 90-ft. building, the angle of elevation of the top of a taller building is 49 and the angle of
depression of the base of this building is 65. Determine the height of the taller building to the nearest foot.
49°
65°
90 ft.
a. 248 ft.
b. 112 ft.
c. 128 ft.
d. 325 ft.
____ 38. Calculate the measure of ABC to the nearest tenth of a degree.
A
13 cm
9 cm
B
D
3 cm
C

a.
b. 116.1
c. 63.9
d.

Short Answer
39. A road increases 8 m in altitude for every 100 m of horizontal distance. Calculate the angle of inclination of
the road, to the nearest tenth of a degree.
40. Determine the height of this isosceles triangle to the nearest tenth of a centimetre.
17°
|
|
18.0 cm
41. Determine the length of WX to the nearest tenth of a centimetre.
W
7.5 cm
32°
Z
X
28°
Y
42. Calculate the measure of ABC to the nearest degree.
B
9 cm
A
8 cm
11 cm
C
43. Francis wants to know the distance between the points where two guy wires are attached to a pole. The guy
wires are anchored to the ground at the same point, 9.0 m from the base of the pole. The angle of inclination
of the longer wire is 61° and the angle of inclination of the shorter wire is 44°. To the nearest tenth of a metre,
how far apart are the points where the guy wires are attached to the pole?
44. From the roof of Yee’s building, the angle of elevation of the top of a taller building is 35°. The angle of
depression of the base of the building is 26°. The buildings are 18 m apart. Determine the height of the taller
building to the nearest metre.
Problem
45. In the diagram below, a Coast Guard patrol boat is at C, which is 11.7 km south of Point Atkinson lighthouse.
A sailboat in distress is at A, which is 8.8 km west of the lighthouse.
a) How far is the patrol boat from the sailboat, to the nearest tenth of a kilometre?
b) At what angle to BC should the patrol boat travel to reach the sailboat? Give the answer to the nearest tenth
of a degree.
8.8 km
A
B
11.7 km
C
46. Determine the measures of
and
5
D
to the nearest tenth of a degree.
C
8
A
B
47. A guy wire is connected from a tower to the ground. Determine the height of the tower, to the nearest tenth of
a metre. What assumptions about the ground are you making?
A
51°
E 30.1 m
D
48. Determine the area of ABC to the nearest tenth of a square unit. Determine its perimeter to the nearest tenth
of a unit.
C
59°
23.1
A
B
49. Calculate the area, to the nearest tenth of a square centimetre, of the circle inscribed in the equilateral triangle
below.
B
30°
13.9cm
A
C
50. Sue used a clinometer to sight the top of a tall building from a point 120.0 m from the base of the building.
The angle shown on the protractor was 48°. Sue held the clinometer 1.7 m above the ground. Determine the
height of the building to the nearest tenth of a metre.
51. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the
same. Is the student correct? Justify your answer.
51 m
46 m
34 m
37 m
52. Determine the perimeter of this triangle to the nearest tenth of a centimetre.
A
\
/
9.0 cm
B
34°
C
D
53. A rectangular lawn has the dimensions shown. A gardener wants to use an electric lawnmower to mow the
lawn. The electrical outlet is located at O.
30.0 m
A
C
8.0 m
27°
N
O
B
a) Determine the length of cord needed to reach corner C, to the nearest tenth of a metre.
b) Determine the distance between the electrical outlet and corner N, to the nearest tenth of a metre.
54. Solve LMN. Give the measures to the nearest tenth. Explain your strategy.
M
L
4.9 cm
8.1 cm
N
55. Solve XYZ. Give the measures to the nearest tenth. Explain your strategy.
X
Y
17.7 cm
47°
Z
56. A Girl Guide measured the angle of elevation of the top of a monument as 57 The height of the monument is
48.5 m. She then walked 46.0 m due west from the point where she measured the angle of elevation.
Determine the angle of elevation of the monument from her new location to the nearest tenth of a degree.
48.5 m
57°
46.0 m
57. Determine the area of this triangle to the nearest tenth of a square centimetre.
135°
21.5 cm
|
|
Unit 2 - Review for Final Exam
Answer Section
MULTIPLE CHOICE
1. ANS:
LOC:
2. ANS:
LOC:
3. ANS:
LOC:
4. ANS:
LOC:
5. ANS:
LOC:
6. ANS:
LOC:
7. ANS:
LOC:
8. ANS:
REF:
TOP:
9. ANS:
REF:
TOP:
10. ANS:
REF:
TOP:
11. ANS:
REF:
TOP:
12. ANS:
REF:
TOP:
13. ANS:
REF:
TOP:
14. ANS:
REF:
TOP:
15. ANS:
REF:
TOP:
16. ANS:
LOC:
17. ANS:
LOC:
18. ANS:
C
PTS: 1
DIF: Easy
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
2.3 Math Lab: Measuring an Inaccessible Height
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
2.3 Math Lab: Measuring an Inaccessible Height
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
REF: 2.4 The Sine and Cosine Ratios
LOC:
19. ANS:
LOC:
20. ANS:
LOC:
21. ANS:
LOC:
22. ANS:
REF:
LOC:
23. ANS:
REF:
LOC:
24. ANS:
REF:
LOC:
25. ANS:
REF:
LOC:
26. ANS:
REF:
LOC:
27. ANS:
REF:
LOC:
28. ANS:
REF:
LOC:
29. ANS:
REF:
LOC:
30. ANS:
REF:
TOP:
31. ANS:
REF:
TOP:
32. ANS:
REF:
TOP:
33. ANS:
REF:
TOP:
34. ANS:
REF:
LOC:
35. ANS:
REF:
LOC:
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
36. ANS:
REF:
LOC:
37. ANS:
REF:
LOC:
38. ANS:
REF:
LOC:
B
PTS: 1
DIF: Easy
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
SHORT ANSWER
39. ANS:
4.6°
PTS: 1
LOC: 10.M4
40. ANS:
17.8 cm
DIF: Moderate
REF: 2.1 The Tangent Ratio
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
DIF: Difficult
REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Procedural Knowledge
41. ANS:
13.5 cm
PTS: 1
DIF: Moderate
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Procedural Knowledge
42. ANS:
92
PTS: 1
DIF: Easy
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Procedural Knowledge
43. ANS:
7.5 m
PTS: 1
DIF: Moderate
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Procedural Knowledge
44. ANS:
21 m
PTS: 1
DIF: Moderate
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Procedural Knowledge
PROBLEM
45. ANS:
a)
Use the Pythagorean Theorem in right ABC.
The Coast Guard patrol boat is approximately 14.6 km from the sailboat.
b)
Use the tangent ratio in right ABC.
The patrol boat should travel at an angle of approximately 36.9 to BC to reach the sailboat.
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
46. ANS:
Determine the measure of
in right BDC.
Determine the measure of
.
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
47. ANS:
In right AED, side DE is opposite A and AE is adjacent to A.
Solve the equation for AE.
The height of the tower is approximately 24.4 m.
I am assuming the ground is horizontal.
PTS: 1
DIF: Moderate
REF: 2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Communication | Problem-Solving Skills
48. ANS:
Determine the length of AB.
In right ABC, AB is opposite C and BC is adjacent to C.
Solve the equation for AB.
Find the area of ABC.
The area of ABC is approximately 444.0 square units.
Determine the length of AC.
Use the Pythagorean Theorem in right ABC.
The perimeter of ABC is:
The perimeter of ABC is approximately 106.4 units.
PTS: 1
DIF: Difficult
REF: 2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
49. ANS:
In right ACB, BC is opposite A and AC is adjacent to A.
Solve the equation for BC.
BC is the radius, r.
The area of the circle is approximately 202.3 cm .
PTS: 1
DIF: Moderate
REF: 2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
50. ANS:
Sketch and label a diagram to represent the information in the problem.
In right ABC, BC is opposite A and AC is adjacent to A.
The angle between the horizontal and the line
B
of sight is:
A
42°
C
120.0 m
1.7 m
D
Solve this equation for BC.
Find the height, h, of the building.
The height of the building is approximately 109.7 m.
PTS: 1
DIF: Difficult
REF: 2.3 Math Lab: Measuring an Inaccessible Height
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
51. ANS:
C in right ABC is the angle of inclination
D
of the guy wire attached to the shorter
building.
A
51 m
In right ABC:
46 m
34 m
B
C
E
37 m
F
The angle of inclination of the guy wire attached to the shorter building is approximately 47.7°.
F in right DEF is the angle of inclination of the guy wire attached to the taller building.
In right DEF:
The angle of inclination of the guy wire attached to the taller building is approximately 43.5°.
The student is not correct. The angles of inclination are different.
PTS: 1
DIF: Difficult
REF: 2.4 The Sine and Cosine Ratios
LOC: 10.M4
TOP: Measurement
KEY: Communication | Problem-Solving Skills
52. ANS:
In right ACD, AD is the hypotenuse, AC is opposite D, and CD is adjacent to D. To determine the
length of AD, use the sine ratio.
Solve this equation for AD.
To determine the length of CD, use the cosine ratio.
Solve this equation for CD.
Since AD = AB and CD = BC, the perimeter, P, of the triangle is:
he perimeter of the triangle is approximately 58.9 cm.
PTS: 1
DIF: Difficult
REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
53. ANS:
a) In right CBO, OC is the hypotenuse, CB is opposite O, and BO is adjacent to O. To determine the
length of OC, use the sine ratio.
Solve this equation for OC.
The length of cord needed to reach corner C is approximately 17.6 m.
b) In right CBO, OC is the hypotenuse, CB is opposite O, and BO is adjacent to O. To determine the
length of BO, use the cosine ratio.
Solve this equation for BO.
To determine the distance between the electrical outlet and corner N, subtract BO from BN.
The distance between the electrical outlet and corner N is approximately 14.3 m.
PTS: 1
DIF: Difficult
REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
54. ANS:
Determine the length of LM first.
Use the Pythagorean Theorem in right LMN.
LM is approximately 6.4 cm.
Determine the measure of N.
Since MN is adjacent to N and LN is the hypotenuse, use the cosine ratio.
N is approximately 52.8° and L is approximately 37.2°.
PTS: 1
DIF: Moderate
REF: 2.6 Applying the Trigonometric Ratios
LOC: 10.M4
TOP: Measurement
KEY: Communication | Problem-Solving Skills
55. ANS:
The acute angles in a right triangle have a sum of 90°.
In right XYZ:
Determine the length of XY.
Since XY is opposite Z and YZ is adjacent to Z, use the tangent ratio.
XY is approximately 19 cm.
Determine the length of XZ.
Since YZ is adjacent to Z and XZ is the hypotenuse, use the cosine ratio.
XZ is approximately 26 cm.
PTS: 1
DIF: Moderate
REF: 2.6 Applying the Trigonometric Ratios
LOC: 10.M4
TOP: Measurement
KEY: Communication | Problem-Solving Skills
56. ANS:
Label a diagram.
Use right ACD to calculate the length of
A
CD. AD is opposite ACD and CD is
adjacent to ACD.
So, use the tangent ratio.
48.5 m
C 57°
B
46.0 m
D
Use right ABD to calculate the measure of B.
First determine the length of BD.
Determine the measure of B.
AD is opposite B and BD is adjacent to B.
So, use the tangent ratio.
he angle of elevation of the monument from the new location is approximately 32.0.
PTS: 1
DIF: Moderate
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
57. ANS:
Label a diagram.
ABD is an isosceles triangle, so each base
angle is:
A
135°
21.5 cm
B
Determine the height, AC, of the triangle.
In right ABC, AC is opposite B and AB is
the hypotenuse.
So, use the sine ratio in ABC.
|
22.5°
|
22.5°
C
D
Determine the length of the base, BD, of ABD
BD = 2(BC)
In right ABC, BC is adjacent to B and AB is the hypotenuse.
So, use the cosine ratio in ACB.
The base, BD, is:
The formula for Area, A, of a triangle is:
The area of the triangle is approximately 163.4 cm2.
PTS: 1
DIF: Difficult
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills