Name: ________________________ Class: ___________________ Date: __________
Foundations and Pre-calculus Mathematics 10
ID: A
PRACTICE TEST: Chapter 8 - Trigonometry
Short Answer
1. Determine tan Q and tan R.
2. Determine the measure of ∠D to the nearest tenth of a degree.
3. Determine the measure of ∠ABD to the nearest tenth of a degree.
4. A ladder leans against the side of a building. The top of the ladder is 5.5 m from the ground. The base of the
ladder is 1.5 m from the wall. What angle, to the nearest degree, does the ladder make with the ground?
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Name: ________________________
ID: A
5. Determine the tangent ratio for ∠K.
6. A guy wire is attached to a tower at a point that is 13 m above the ground. The wire is anchored 22 m from
the base of the tower. What angle, to the nearest degree, does the guy wire make with the ground?
7. Determine the length of side z to the nearest tenth of a centimetre.
8. Determine the length of side d to the nearest tenth of a centimetre.
9. A guy wire is attached to a tower at a point that is 6.1 m above the ground. The angle between the wire and
the level ground is 52°. How far from the base of the tower is the wire anchored to the ground, to the nearest
tenth of a metre?
10. A flagpole casts a shadow that is 18 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.
11. A surveyor held a clinometer 1.6 m above the ground from a point 40.0 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.
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Name: ________________________
ID: A
12. Determine sin A and cos A to the nearest tenth.
13. Determine the measure of ∠D to the nearest tenth of a degree.
14. A helicopter is hovering 250 m above a road. A car stopped on the side of the road is 350 m from the
helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree?
15. Determine the measure of ∠Y to the nearest tenth of a degree.
16. A rope that anchors a hot air balloon to the ground is 141 m long. The balloon is 63 m above the ground.
What is the angle of inclination of the rope to the nearest tenth of a degree?
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Name: ________________________
ID: A
17. Determine the length of MN to the nearest tenth of an centimetre.
18. Determine the length of RS to the nearest tenth of a metre.
19. From the start of a runway, the angle of elevation of an approaching airplane is 18.5°. At this time, the plane
is flying at an altitude of 8.2 km. How far is the plane from the start of the runway to the nearest tenth of a
kilometre?
20. A tree broke 11 ft. above the ground. The top of the tree now touches the level ground and the trunk is still
partially attached to the stump. The angle of inclination of the tree is 41°. To the nearest foot, determine the
height of the tree before it broke.
21. Solve this right triangle. Give the measures to the nearest tenth.
22. The front of a tent has the shape of an isosceles triangle with equal sides 174 cm long. The measure of the
angle at the peak of the tent is 109°. Calculate the maximum headroom in the tent to the nearest centimetre.
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Name: ________________________
ID: A
23. Determine the length of RS to the nearest tenth of a centimetre.
24. Calculate the measure of ∠GHJ to the nearest tenth of a degree.
25. From the top of an 90-ft. building, the angle of elevation of the top of a taller building is 59° and the angle of
depression of the base of this building is 68°. Determine the height of the taller building to the nearest foot.
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Name: ________________________
ID: A
Problem
26. Calculate the area, to the nearest tenth of a square centimetre, of the circle inscribed in the equilateral triangle
below.
27. Determine the perimeter of this triangle to the nearest tenth of a centimetre.
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ID: A
PRACTICE TEST: Chapter 8 - Trigonometry
Answer Section
SHORT ANSWER
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.
tan Q = 1.5; tan R = 0.6
28.3°
66.0°
75°
143
24
31°
7.5 cm
21.2 cm
4.8 m
20 m
17.0 m
sin A = 0.3; cos A = 0.9
28.7°
46°
63.0°
26.5°
9.3 cm
24.9 m
25.8 km
28 ft.
∠F = 65°; GH = 12.9 m; FH = 14.2 m
101 cm
7.3 cm
55.3°
141 ft.
1
ID: A
PROBLEM
26. In right ∆ACB, BC is opposite ∠A and AC is adjacent to ∠A.
opposite
tan A =
adjacent
tan A =
BC
AC
BC
9.5
Solve the equation for BC.
BC
9.5tan30° = 9.5
9.5
tan30° =
9.5tan30° = BC
BC = 5.4848. . .
BC is the radius, r.
A = πr 2
A = π (5.4848. . . ) 2
A = 94.5095. . .
The area of the circle is approximately 94.5 cm 2 .
2
ID: A
27. 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
sin40° =
15.0
AD
Solve this equation for AD.
AD sin40° =
(15.0)(AD)
AD
AD sin40° = 15.0
15.0
AD sin40°
=
sin 40°
sin40°
AD =
15.0
sin40°
AD = 23.3358. . .
To determine the length of CD, use the cosine ratio.
cos D =
adjacent
hypotenuse
cos D =
CD
AD
cos 40° =
CD
23.3358. . .
Solve this equation for CD.
(23.3358. . . ) cos 40° =
(23.3358. . . )(CD)
23.3358. . .
(23.3358. . . ) cos 40° = CD
CD = 17.8763. . .
Since AD = AB and CD = BC, the perimeter, P, of the triangle is:
P = AD + AB + CD + BC
P = 23.3358… + 23.3358… + 17.8763… + 17.8763…
P = 82.4243…
3
ID: A
Τhe perimeter of the triangle is approximately 82.4 cm.
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