1
Math 1201 Sample Test – Trigonometry
Multiple Choice Questions Place the letter that corresponds with the correct answer in
the space provided to the right. (10 marks)
1. What is the measure of
X
to the nearest degree if
4
sin
9
X
? 1._____
a)
7
o
b)
64
o
c)
26
o
d)
83
o
2. What is the measure of
A
to the nearest degree? 2._____
a)
61
o
b)
29
o
c)
40
o
d)
50
o
3. What is the length of MA to the nearest tenth? 3._____
a) 0.1 cm
b) 3.5 cm
c) 17.0 cm
d) 7.7 cm
4. What is the correct ratio for
sin A
? 4._____
a)
5
12
b)
12
13
c)
5
13
d)
13
12
5. In which of the following triangles is cos B = 0.8? 5._____
a)
b)
c)
d)
4
5
A
C
B
5
8
B
C
A
4
5
B
C
A
4
5
B
C
A
2
6. What is the area of
PQR
below? 6.____
a) 15.8 m
b)
2
31.2m
c)
2
66.4m
d)
2
16.6m
7. A student sees a bird on top of a 12m high light pole. The student is standing 7.____
20m from the base of the pole. At what angle must the student incline her
camera to take a picture of the bird?
a) 31
0
b) 37
0
c) 59
0
d) 87
0
8. An airplane approaches an airport. At a certain time, the plane is 1020m high. 8.____
Its angle of elevation measured from the airport is
20.5
o
. How far is the plane
from the airport to the nearest meter?
a) 2728 m b) 2913 m
c) 1089 m d) 3 m
9. Which of the following statements is true of the diagram below? 9.____
a)
8
cos
15
P
b)
15
tan
8
Q
c)
8
sin
17
P
d)
15
cos
17
Q
10. Which of the following is not correct to the nearest hundredth? 10.____
a)
sin75 0.97
o
b)
tan37 0.75
o
c)
tan18 0.23
o
d)
cos46 0.69
o
Short Answer Questions Complete each of the following in the space provided. Be sure
to show all necessary steps.
1. Find the value of x in each of the following diagrams. Give answers to the nearest tenth.
(6 marks)
a) b) c)
3
2. Thomas stood 12.0 m from the base of a tree. He used a clinometer to sight the top of the
tree. The angle shown on the clinometer was 70°. Thomas held the clinometer 2.2 m about
the ground. Determine the height of the tree to the nearest tenth of a metre. (3 marks)
3. Solve the following triangle. Give the side lengths to the nearest tenth of a centimeter and
the angle measures to the nearest degree. (5 marks)
4. A traffic helicopter is patrolling the air. The chopper is 630m above the highway. An
accident is located at an angle of depression of 27
o
from the chopper. How far along the
highway is the accident? Include a sketch. (3 marks)
5. A person stands at a window on the 9
th
floor of an office building. He measures the angle
of elevation to be
25
o
and the angle of depression to be
36
o
of the top and the base of a
tower. The person knows that he made the measurements 40 m above the ground.
Determine the height of the tower to the nearest tenth of a metre.
