Download Unit 2 Review

Name: ________________________ Class: ___________________ Date: __________
Math 10 - Unit 2 Final Review Worksheet - Trigonometry
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine sin G and cos G to the nearest hundredth.
a.
b.
____
c.
d.
sin G = 1.01; cos G = 0.15
sin G = 0.99; cos G = 0.15
c.
d.
tan A = 0.8; tan C = 1.25
tan A = 0.6247...; tan C = 1.25
c.
35
37
2. Determine tan A and tan C.
a.
b.
____
sin G = 0.99; cos G = 6.54
sin G = 0.15; cos G = 0.99
tan A = 1.25; tan C = 0.8
tan A = 0.8; tan C = 0.7809...
3. Determine the tangent ratio for ∠T.
a.
12
35
b.
37
35
1
d.
35
12
ID: A
Name: ________________________
____
4. Determine tan Q and tan R.
a.
b.
____
tan Q = 0.428571; tan R = 0.75
tan Q = 1.3; tan R = 0.75
c.
d.
tan Q = 1.3; tan R = 0.571428
tan Q = 0.75; tan R = 1.3
c.
d.
sin A = 0.6; cos A = 1.3
sin A = 0.6; cos A = 0.8
c.
37
12
5. Determine sin A and cos A to the nearest tenth.
a.
b.
____
ID: A
sin A = 1.7; cos A = 0.8
sin A = 0.8; cos A = 0.6
6. Determine the tangent ratio for ∠K.
a.
12
35
b.
12
37
2
d.
35
12
Name: ________________________
____
7. Determine the measure of ∠N to the nearest tenth of a degree.
a.
____
57.4°
b.
61.7°
c.
32.6°
d.
28.3°
d.
71.6°
d.
24.9°
8. Determine the measure of ∠D to the nearest tenth of a degree.
a.
____
ID: A
18.4°
b.
19.5°
c.
70.5°
9. Determine the measure of ∠Y to the nearest tenth of a degree.
a.
27.6°
b.
62.4°
c.
3
65.1°
Name: ________________________
ID: A
____ 10. Determine the measure of ∠Q to the nearest tenth of a degree.
a.
68.4°
b.
69.8°
c.
21.6°
d.
20.2°
d.
20.9°
d.
24.9°
d.
53.9°
____ 11. Determine the measure of ∠D to the nearest tenth of a degree.
a.
67.6°
b.
69.1°
c.
22.4°
____ 12. Determine the measure of ∠ABD to the nearest tenth of a degree.
a.
65.1°
b.
67.2°
c.
22.8°
____ 13. Determine the measure of ∠V to the nearest tenth of a degree.
a.
59.5°
b.
36.1°
c.
4
30.5°
Name: ________________________
ID: A
____ 14. Determine the measure of ∠B to the nearest tenth of a degree.
a.
94.3°
b.
34.2°
c.
42.8°
d.
47.2°
d.
64.3 m
d.
3.7 cm
d.
13.9 cm
____ 15. Determine the length of RS to the nearest tenth of a metre.
a.
19.7 m
b.
5.7 m
c.
18.0 m
____ 16. Determine the length of side d to the nearest tenth of a centimetre.
a.
29.5 cm
b.
27.7 cm
c.
10.7 cm
____ 17. Determine the length of DE to the nearest tenth of a centimetre.
a.
8.8 cm
b.
15.9 cm
c.
5
3.7 cm
Name: ________________________
ID: A
____ 18. Determine the length of side z to the nearest tenth of a centimetre.
a.
9.7 cm
b.
2.6 cm
c.
5.4 cm
d.
8.5 cm
d.
16.8 cm
d.
5.0 m
d.
19.9 cm
____ 19. Determine the length of MN to the nearest tenth of an centimetre.
a.
36.9 cm
b.
41.4 cm
c.
8.5 cm
____ 20. Determine the length of side l to the nearest tenth of a metre.
a.
5.4 m
b.
27.4 m
c.
11.1 m
____ 21. Determine the length of XY to the nearest tenth of a centimetre.
a.
8.4 cm
b.
15.2 cm
c.
6
31.4 cm
Name: ________________________
ID: A
____ 22. Determine the length of side s to the nearest tenth of a millimetre.
a.
18.4 mm
b.
43.5 mm
c.
8.6 mm
d.
9.5 mm
d.
3.1 m
____ 23. Calculate the length of this rectangle to the nearest tenth of a metre.
a.
7.9 m
b.
2.9 m
c.
6.7 m
____ 24. Determine the angle of inclination of the line to the nearest tenth of a degree.
a.
63.3°
b.
24.2°
c.
65.8°
d.
26.7°
____ 25. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 22%.
a. 77.3°
b. 77.6°
c. 12.4°
d. 12.7°
____ 26. A guy wire is attached to a tower at a point that is 10 m above the ground. The wire is anchored 21 m from
the base of the tower. What angle, to the nearest degree, does the guy wire make with the ground?
a. 62°
b. 25°
c. 28°
d. 65°
____ 27. 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.
7
3.7 m
d.
8.2 m
Name: ________________________
ID: A
____ 28. A 55-ft. guy wire helps to support a tower. The wire is anchored to the ground 37 ft. from the base of the
tower. What is the measure of the angle formed between the wire and the ground, to the nearest degree?
a.
48°
b.
56°
c.
34°
d.
42°
____ 29. 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 7.7 km. How far is the plane from the start of the runway to the nearest tenth of a
kilometre?
a.
8.1 km
b.
2.3 km
c.
25.6 km
d.
24.4 km
____ 30. A ladder leans against the side of a building. The top of the ladder is 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. 79°
b. 11°
c. 9°
d. 83°
____ 31. A helicopter is hovering 200 m above a road. A car stopped on the side of the road is 300 m from the
helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree?
a.
56°
b.
48°
c.
42°
d.
34°
____ 32. A student stood 8.0 m from the base of a tree. She used a clinometer to sight the top of the tree. The angle
shown on the protractor scale was 65°. The student held the clinometer 1.6 m above the ground. Determine
the height of the tree to the nearest tenth of a metre.
a.
10.4 m
b.
5.3 m
c.
3.7 m
d.
18.8 m
____ 33. This cabin’s roof is built within 1° of the recommended angle for solar panels. Determine the approximate
latitude of the cabin, to the nearest degree.
a.
50°
b.
34°
c.
40°
d.
56°
____ 34. 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.
8
19 ft.
d.
23 ft.
Name: ________________________
ID: A
____ 35. 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
____ 36. A ladder is 13.0 m long. It leans against a wall. The base of the ladder is 3.7 m from the wall. What is the
angle of inclination of the ladder to the nearest tenth of a degree?
a.
73.5°
b.
16.5°
c.
74.1°
d.
15.9°
____ 37. 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
____ 38. Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at
point C. Determine the angle, to the nearest degree, between her path and the longest side of the playground.
a.
37°
b.
41°
c.
53°
d.
49°
____ 39. 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
____ 40. A wheelchair ramp is 7.0 m long. Its angle of inclination is 9°. Calculate the rise of the ramp to the nearest
tenth of a metre.
a.
1.0 m
b.
44.7 m
c.
9
1.1 m
d.
6.9 m
Name: ________________________
ID: A
____ 41. A surveyor made the measurements shown in the diagram. Determine the distance from R to S, to the nearest
hundredth of a metre.
a.
46.66 m
b.
70.50 m
c.
25.75 m
d.
58.79 m
____ 42. 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
d.
62.5°
____ 43. Determine the measure of ∠DBC to the nearest tenth of a degree.
a.
27.5°
b.
24.8°
c.
65.2°
____ 44. A helicopter is ascending vertically. On the ground, a searchlight is 125 m from the point where the
helicopter lifted off the ground. It shines on the helicopter and the angle the beam makes with the ground is
48°. How high is the helicopter at this point, to the nearest metre?
a.
187 m
b.
93 m
c.
10
113 m
d.
139 m
Name: ________________________
ID: A
____ 45. Solve this right triangle. Give the measures to the nearest tenth.
a.
b.
∠U = 26.6°; ∠W = 63.4°; UW = 14.5 cm c.
∠U = 63.4°; ∠W = 26.6°; UW = 14.5 cm d.
∠U = 63.4°; ∠W = 26.6°; UW = 29.1 cm
∠U = 26.6°; ∠W = 63.4°; UW = 29.1 cm
____ 46. Solve this right triangle. Give the measures to the nearest tenth.
a.
b.
∠J = 68.6°; ∠L = 21.4°; JL = 24.7 cm
∠J = 68.6°; ∠L = 21.4°; JL = 63.1 cm
c.
d.
∠J = 21.4°; ∠L = 68.6°; JL = 24.7 cm
∠J = 21.4°; ∠L = 68.6°; JL = 63.1 cm
____ 47. Solve this right triangle. Give the measures to the nearest tenth.
a.
b.
∠F = 67°; GH = 3.4 m; FH = 8.7 m
∠F = 67°; GH = 18.8 m; FH = 8.7 m
c.
d.
11
∠F = 77°; GH = 18.8 m; FH = 20.5 m
∠F = 67°; GH = 18.8 m; FH = 20.5 m
Name: ________________________
ID: A
____ 48. Solve this right triangle. Give the measures to the nearest tenth.
a.
b.
∠G = 40°; GH = 21.8 cm; FH = 18.3 cm
∠G = 40°; GH = 21.8 cm; FH = 44.3 cm
c.
d.
∠G = 40°; GH = 18.3 cm; FH = 21.8 cm
∠G = 50°; GH = 21.8 cm; FH = 18.3 cm
____ 49. An architect draws this diagram of a wheelchair entrance ramp for a building. Determine the angle of
inclination of the ramp to the nearest tenth of a degree.
a.
86.7°
b.
29.7°
c.
3.3°
d.
5.1°
____ 50. At a point 25 ft. from the base of a totem pole, the angle of elevation of the top of the pole is 50.1°. How tall
is the totem pole to the nearest foot?
a.
39 ft.
b.
16 ft.
c.
30 ft.
d.
21 ft.
____ 51. A water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. It then travels 15 km due
east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the
path it took due east and the path it will take to return directly to its dock?
a.
25°
b.
62°
c.
28°
d.
65°
____ 52. A road rises 1 m for every 19 m measured along the road. To the nearest metre, how far does a car travel
horizontally when it travels 300 m along the road?
a.
300 m
b.
16 m
c.
12
19 m
d.
300 m
Name: ________________________
ID: A
____ 53. The front of a tent has the shape of an isosceles triangle with equal sides 163 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.
a.
129 cm
____ 54. Determine the area of
a.
291 cm2
b.
125 cm
c.
99 cm
d.
231 cm
d.
208 cm2
RST to the nearest square centimetre.
b.
707 cm2
c.
104 cm2
____ 55. Determine the perimeter of an equilateral triangle with height 11.9 cm. Give the measure to the nearest tenth
of a centimetre.
a.
81.8 cm
b.
41.2 cm
c.
30.9 cm
d.
71.4 cm
____ 56. Determine the area of this rectangle to the nearest tenth of a square metre.
a.
54.0 m2
b.
420.2 m2
c.
13
98.1 m2
d.
61.9 m2
Name: ________________________
ID: A
____ 57. Determine the length of RS to the nearest tenth of a centimetre.
a.
6.7 cm
b.
9.3 cm
c.
11.4 cm
d.
8.3 cm
d.
4.5 cm
____ 58. Determine the length of MN to the nearest tenth of a centimetre.
a.
5.2 cm
b.
3.4 cm
c.
2.9 cm
____ 59. Two trees are 55 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?
a.
b.
33 yd.; 31 yd.
19 yd.; 15 yd.
c.
d.
14
41 yd.; 50 yd.
40 yd.; 49 yd.
Name: ________________________
ID: A
____ 60. Determine the length of QR to the nearest metre.
a.
85 m
b.
170 m
c.
127 m
d.
118 m
d.
68.0°
____ 61. Calculate the measure of ∠GHJ to the nearest tenth of a degree.
a.
77.5°
b.
29.3°
c.
60.7°
____ 62. From the top of an 80-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 62°. Determine the height of the taller building to the nearest foot.
a.
211 ft.
b.
112 ft.
c.
15
129 ft.
d.
276 ft.
Name: ________________________
ID: A
____ 63. Calculate the measure of ∠ABC to the nearest tenth of a degree.
a.
47.7°
b.
102.5°
c.
77.5°
d.
52.6°
d.
41.9 cm
____ 64. Determine the length of AC to the nearest tenth of a centimetre.
a.
70.4 cm
b.
141.6 cm
c.
39.9 cm
Short Answer
65. Determine the height of this isosceles triangle to the nearest tenth of a centimetre.
66. Tan B = 1.3; determine the measure of ∠B to the nearest tenth of a degree.
67. 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.
16
Name: ________________________
ID: A
68. Determine the angle of inclination of the line to the nearest tenth of a degree.
69. On a clinometer, how does the acute angle between the thread and the straw relate to the angle of inclination
of the straw?
Problem
70. Determine the perimeter of this triangle to the nearest tenth of a centimetre.
71. 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.
17
Name: ________________________
ID: A
72. Calculate the angle of inclination of the roof to the nearest tenth of a degree.
73. A Girl Guide measured the angle of elevation of the top of a monument as 59°. The height of the monument
is 38.5 m. She then walked 31.0 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.
74. Determine the area of this triangle to the nearest tenth of a square centimetre.
75. The length of the body diagonal in this rectangular prism is 61 cm. The width of the prism is 29 cm. The
measure of ∠AFH is 23°. Determine the height and the length of the rectangular prism to the nearest
centimetre.
18
ID: A
Math 10 - Unit 2 Final Review Worksheet - Trigonometry
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
D
C
D
B
D
D
D
A
B
A
C
B
D
C
A
B
B
D
C
A
B
D
C
B
C
B
C
A
C
A
C
B
A
A
C
A
D
A
C
1
ID: A
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
C
B
D
B
D
B
C
D
A
C
C
A
D
C
C
B
A
D
A
B
D
C
C
D
D
SHORT ANSWER
65.
66.
67.
68.
69.
23.4 cm
∠B Ö
= 52.4°
4.6°
55.1°
The angle of inclination of the straw is equal to 90° minus the angle between the thread and the straw.
2
ID: A
PROBLEM
70. 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.
sinD =
opposite
hypotenuse
sinD =
AC
AD
sin34° =
9.0
AD
Solve this equation for AD.
AD sin34° =
(9.0)(AD)
AD
AD sin34° = 9.0
AD sin34°
9.0
=
sin 34°
sin34°
AD =
9.0
sin34°
AD = 16.0946. . .
To determine the length of CD, use the cosine ratio.
cos D =
adjacent
hypotenuse
cos D =
CD
AD
cos 34° =
CD
16.0946. . .
Solve this equation for CD.
(16.0946. . . ) cos 34° =
(16.0946. . . )(CD)
16.0946. . .
(16.0946. . . ) cos 34° = CD
CD = 13.3430. . .
Since AD = AB and CD = BC, the perimeter, P, of the triangle is:
3
ID: A
P = AD + AB + CD + BC
P = 16.0946… + 16.0946… + 13.3430… + 13.3430…
P = 58.8753…
Τhe perimeter of the triangle is approximately 58.9 cm.
71.
∠C in right ∆ABC is the angle of inclination
of the guy wire attached to the shorter
building.
In right ∆ABC:
opposite
sinC =
hypotenuse
sinC =
AB
AC
sinC =
35
47
∠C = 48.1316. . . °
The angle of inclination of the guy wire attached to the shorter building is approximately 48.1°.
∠F in right ∆DEF is the angle of inclination of the guy wire attached to the taller building.
In right ∆DEF:
adjacent
cos F =
hypotenuse
cos F =
EF
DF
cos F =
37
52
∠F = 44.6397. . . °
The angle of inclination of the guy wire attached to the taller building is approximately 44.6°.
The student is not correct. The angles of inclination are different.
4
ID: A
72.
Draw a diagram to represent the cross-section
of the roof.
Find BC.
22 ft.
BC =
2
BC = 11 ft.
In right ∆ABC:
adjacent
cos C =
hypotenuse
cos C =
BC
AC
cos C =
11
12
∠C = 23.5564. . . °
The angle of inclination of the roof is approximately 23.6°.
5
ID: A
73. Label a diagram.
Use right ∆ACD to calculate the length of
CD. AD is opposite ∠ACD and CD is
adjacent to ∠ACD.
So, use the tangent ratio.
opposite
tan C =
adjacent
tan C =
AD
CD
tan59° =
38.5
CD
CD tan59° = 38.5
CD =
38.5
tan59°
CD = 23.1331…
Use right ∆ABD to calculate the measure of ∠B.
First determine the length of BD.
BD = BC + CD
BD = 31.0 + 23.1331…
BD = 54.1331…
Determine the measure of ∠B.
AD is opposite ∠B and BD is adjacent to ∠B.
So, use the tangent ratio.
opposite
tanB =
adjacent
tanB =
AD
BD
tanB =
38.5
54.1331…
∠B = 35.4207…°
Τhe angle of elevation of the monument from the new location is approximately 35.4°.
6
ID: A
74. Label a diagram.
∆ABD is an isosceles triangle, so each base
angle is:
180° − 129°
=
2
= 25.5°
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.
opposite
sinB =
hypotenuse
sinB =
sin25.5° =
AC
AB
AC
22.1
22.1 sin25.5° = AC
AC = 9.5142…
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.
adjacent
cos B =
hypotenuse
cos B =
cos 25.5° =
BC
AB
BC
22.1
22.1 cos 25.5° = BC
BC = 19.9471…
The base, BD, is:
BD = 2(BC)
BD = 2(19.9471…)
BD = 39.8942…
The formula for Area, A, of a triangle is:
7
ID: A
A=
1
bh
2
A=
1
(39.8942…)(9.5142…)
2
A = 189.7829…
The area of the triangle is approximately 189.8 cm2.
8
ID: A
75.
Determine the height of the prism.
In right ∆!AHF, the height, AH, is opposite
∠AFH and AF is the hypotenuse.
Use the sine ratio in ∆AHF.
opposite
sinF =
hypotenuse
sinF =
AH
AF
sin23° =
AH
61
61sin23° = AH
AH = 23.8345…
The height of the prism is approximately 24 cm.
Determine the length of the prism.
In right ∆AHF, FH is adjacent to ∠AFH and AF is the hypotenuse.
Use the cosine ratio in ∆AHF.
adjacent
cos F =
hypotenuse
cos F =
FH
AF
cos 23° =
FH
61
61cos 23° = FH
FH = 56.1507. . .
Use the Pythagorean Theorem in ∆EHF to determine the length of the prism, EF.
FH 2 = EH 2 + EF 2
56.1507…2 = 29 2 + EF 2
56.1507…2 − 29 2 = EF 2
EF =
56.1507…2 − 29 2
EF = 48.0823…
Τhe length of the prism is approximately 48 cm.
9