FPC Math 10
Trigonometry Test Review.
Name:_____________________
1. For ∠Y in right △XYZ, identify
a) the hypotenuse
b) the adjacent side
c) the opposite side
2. Refer to right △XYZ in question 1.
a) State the tangent ratio of ∠Y.
b) State the tangent ratio of ∠Z.
3. For right △LMN, determine the length n if ∠N = 68° and l = 12.4 cm.
4. Calculate the smallest angle in right △ABC where ∠C = 90°, side a measures 32.7 m, and side
b measures 27.2 m.
5. A ramp on a moving truck forms an angle of 30° with the ground, allowing movers to load heavy
items easily. If the truck bed is 1.35 m above the ground, how far will the ramp extend behind
the truck?
6. The length of a shadow cast by a building is 25 m. Nearby, a 1.8-m shadow is cast by a man who
is 2.2 m tall. Calculate the height of the building.
7. For right △ABC, state each of the following ratios.
a) sin A =
b) cos A =
c) sin B =
d) cos B =
8. Calculate the value of b in △ABC in question 7 if
a) ∠B = 23° and c = 12
b) ∠A = 67° and c = 9.2
9. A ladder 7 m in length is leaning against a wall. The top of the ladder forms an angle of 20° with
the wall. Determine the distance from the bottom of the wall to the bottom of the ladder.
10. Inflatable slides are used to evacuate people from airplanes. If a slide must form an angle of 35°
with the ground and its bottom will be 4.5 m from the plane, what length does the slide need to
be?
11. The length of a ramp from the ground level of a parking garage to the upper level is 54 ft.
a) If the height of the upper level is 8 ft, what angle does the ramp make with the ground?
Round your answers to the nearest tenth of a unit.
b) Over what horizontal distance does the ramp extend?
Round your answers to the nearest tenth of a unit.
12. Solve each triangle, to the nearest tenth of a unit.
13. Consider adjacent right triangles KLM and KMN shown in the figure.
a) What is the height of side h, to the
nearest centimetre?
b) What is the measure of ∠MKN, to the nearest degree?
14. A hot-air balloon is floating 105 metres above a soccer field 100 m long. A photographer in the
balloon’s basket can see the two goalkeepers standing on their goal lines. One is at an angle of
depression of 53.39°. The other is at an angle of depression of 78.17°. If the balloon is directly
between the goalies, how far, to the nearest metre, is each goalie from a point on the ground
directly under the balloon?
Normally you are required to draw your own diagrams, this
time the diagrams are provide.
15. The top of a skyscraper is 200 m above the ground. You are standing 100 m from the base of the
building. Your friend is 20 m behind you. Each of you has a clear view of the top of the
building. Round your answers to the nearest tenth of a unit.
a) What is the distance between the top
of the building and your friend?
b) What is the distance between the top of the skyscraper and you?
c) From your position, at what angle of elevation does the top of the building appear to be?
FPC Math 10
Trigonometry Test Review.
Name:_______Key_______
1. For ∠Y in right △XYZ, identify
a) the hypotenuse
Side x.
b) the adjacent side
Side z.
c) the opposite side
Side y.
2. Refer to right △XYZ in question 1.
a) State the tangent ratio of ∠Y.
tangent Y =
y
z
b) State the tangent ratio of ∠Z.
tangent Z =
z
y
3. For right △LMN, determine the length n if ∠N = 68° and l = 12.4 cm.
tangent 68° =
n
12.4
12.4 · tangent 68° = n ≈ 30.7 cm
4. Calculate the smallest angle in right △ABC where ∠C = 90°, side a measures 32.7 m, and side
b measures 27.2 m.
Since side c is the hypotenuse (longest side among 3 sides)
and side a is smaller than side b, so ∠A < ∠B.
Find ∠A.
tangent A =
∠A ≈ 39.8 °
27.2
32.7
,
1
∠A = tan
27.2
32.7
The smallest angle, ∠A is 39.8 °.
5. A ramp on a moving truck forms an angle of 30° with the ground, allowing movers to load heavy
items easily. If the truck bed is 1.35 m above the ground, how far will the ramp extend behind
the truck?
We are determining the hypotenuse, d.
1.35
1.35
, d=
d
sin 30
sin 30° =
d ≈ 2.7 m
The ramp is 2.7 m long behind the truck.
6. The length of a shadow cast by a building is 25 m. Nearby, a 1.8-m shadow is cast by a man who
is 2.2 m tall. Calculate the height of the building.
1.8 25

2 .2 x
,
x=
25  2.2
 30.6m
1 .8
7. For right △ABC, state each of the following ratios.
a) sin A =
a
c
b) cos A =
b
c
c) sin B =
b
c
d) cos B =
a
c
8. Calculate the value of b in △ABC in question 7 if
a) ∠B = 23° and c = 12
sin 23° =
b
12
,
12 · sin 23° = b
b ≈ 4.7 m
b) ∠A = 67° and c = 9.2
cos 67° =
b
9.2
,
9.2 · cos 67° = b
b ≈ 3.6 m
12. Solve each triangle, to the nearest tenth of a unit.
Solving means finding all the unknown parts of the right triangle with limited
information.
∠B = 90° − 17° = 73.0°
sin 17° =
cos M =
a
,
12.6
∠M = cos 1
tan 48.2° =
b
,
12.6
m
4.8
m = 4.8 · tan 48.2° ≈ 5.4 mm
b = 12.6 · cos 17° ≈ 12.0 cm
13. Consider adjacent right triangles KLM and KMN shown in the figure.
a) What is the height of side h, to the
nearest centimetre?
sin 51° =
h
,
112
h = 112 · sin 51° ≈ 87 cm
b) What is the measure of ∠MKN, to the nearest degree?
tan ∠MKN =
58
87
4 .8
 48.2°
7 .2
∠L = 90° − 48.2° = 41.8°
a = 12.6 · sin 17° ≈ 3.7 cm
cos 17° =
4.8
,
7.2
,
1
∠MKN = tan
58
87
≈ 34°
14. A hot-air balloon is floating 105 metres above a soccer field 100 m long. A photographer in the
balloon’s basket can see the two goalkeepers standing on their goal lines. One is at an angle of
depression of 53.39°. The other is at an angle of depression of 78.17°. If the balloon is directly
between the goalies, how far, to the nearest metre, is each goalie from a point on the ground
directly under the balloon? Find α and β first.
α = 90° − 53.39° = 36.61° ,
tan 36.61° =
x
,
105
β = 90° − 78.17° = 11.83°
x = 105 · tan 36.61°
x ≈ 78 m
tan 11.83° =
y
,
105
y = 105 · tan 11.83°
y ≈ 22 m
15. The top of a skyscraper is 200 m above the ground. You are standing 100 m from the base of the
building. Your friend is 20 m behind you. Each of you has a clear view of the top of the
building. Round your answers to the nearest tenth of a unit.
a) What is the distance between the top
of the building and your friend?
We are determining the hypotenuse in red color and let it be x.
200 2  120 2  233.2 m
x=
b) What is the distance between the top of the skyscraper and you?
We are determining the hypotenuse in blue color and let it be y.
y=
200 2  100 2  223.6 m
c) From your position, at what angle of elevation does the top of the building appear to be?
Let that angle of elevation be β.
tan β =
200
,
100
1
β = tan
200
100
= 63.4°