Download Review Booklet Trigonometry 1. Complete the following for the

\Math 10 Common
Name ________________________
Review Booklet
Trigonometry
1. Complete the following for the indicated trigonometric ratios.
2. Use a calculator to determine the value of each trigonometric ratio to four decimal places.
a. sin68˚ = _______________
b. tan30˚ = _______________
c. cos19˚= _______________
d. cos22˚ = _______________
e. tan85˚ = _______________
f. sin7˚ = ________________
3. In each case determine the indicated acute (less than 90˚) angle to the nearest degree.
a. sinA = 0.6789
 A = ________
b. cosX = 0.1234
 X = ________
c. tanP = 0.55
 P = ________
d. sinK =
2
2
 K = _______
e. cosM =
7
24
 M = _______
f. tanR =
3
 R = _______
4. Determine the length of the indicated side to the nearest 0.1 cm.
5. Determine the measure of the indicated angle to the nearest degree.
6. Solve for angle A to the nearest 0.1˚.
7. Jacob has been given the task of determining the height of a building. He walks 30m
away from the base of the building and uses a clinometer to measure the angle of
elevation to the top of the building to be 58˚. Calculate the height of the building to the
nearest metre.
8. From the top of a vertical cliff 120 metres above sea level, Susan measures the angle of
depression of a boat in the water to be 37˚. To the nearest metre, determine the distance
between the boat and the base of the cliff.
9. A large tree, Tree 1, casts a shown on the ground as shown in the diagram below:
Using the information in the diagram, if Tree 2 is halfway between the base of Tree 1 and
the top of the shadow formed on the ground by Tree 1, what is the height Tree 2?
A helium balloon hovers above a 0.75 meter tall sign. The angle of elevation from the top
of the balloon to a baby sitting 3.6 meters from the base of the sign is 57°, as shown in
the diagram below:
10. Using this information, how high is the top of the balloon over the top of the sign?
11. In triangle XYZ, XY = 5 units, XZ =
value of cosY.
A.
5
75
B.
50
5
C.
75
5
D.
5
50
50 units and YZ = 75 units. Determine the
12. For the right angles triangle ABC, only one of the following ratios is correct. The correct
ratio is
8
15
8
B. cos A 
17
8
C. tan B 
15
15
D. sin B 
17
A. sin A 
13. A corner flag in a World Cup soccer match is 5 feet high. At game time, the flag casts a
shadow which is 3.2 feet long. To the nearest 0.1 degree, the angle of elevation of the
sun is _______.
14. Calculate the measure of  BEC to the nearest degree.
15. Determine the length of PQ, to the nearest 0.1 cm.
16. Determine the measure of angle ABC, to the nearest degree.
17. From the top of a cliff 110 m high an observer sees two boats, one directly behind the
other, heading for shore. The angle of depression from the observer to the boat farther
from the observer is 48˚ and the angle of depression to the nearer boat is 57˚. Calculate
the distance between the boats, to the nearest metre.
18. The diagram shows two marathon runners, A and B, heading towards the finish line of a
race. From an apartment window 80 meters above the ground and 20 meters behind the
finish line, Tony measures the angle of depression of the runners to be 28˚ and 24˚
respectively.
a. Calculate the distance between the runners to the nearest metre.
b. A is travelling at a constant speed of 4.5 m/s while B is travelling at a constant
speed of 5.1 m/s. Which runner till finish the race first?
19. In January 2003 the tallest building in Rockyville was the Metro Building. Recently a
developer was commissioned by the Gammapro Oil Company to build a taller building
next to the Metro Building. From the top of the Metro Building the angle of elevation of
the top of the Gammapro Building is 24˚ and the angle of depression to the foot of the
Gammapro Building is 56˚. If the buildings are 45 m apart determine the height of each
building to the nearest metre.
20. In the diagram, PQ = 16 m, QR = 12 m and PT = TR.
a. Calculate the measure of  QRT to the nearest 0.1˚.
b. Calculate the length of PT to the nearest 0.1 m.
21. In the diagram ABCD represents a rectangular sandbox for kindergarten children to play
in. A teacher stands at the corner of the area to supervise the children. At a certain time
of day the tip of the shadow cast by the teacher on the play area is exactly at M, the
midpoint of CD. If the teacher is 1.8 m tall, calculate the measure of angle EMA, to the
nearest degree.
22. In order to find the height of a tree on the opposite back of a river Jenny makes the
measurements shown on the diagram. Calculate the height of the tree to the nearest
meter.
23. In the diagram determine the height of the tower to the nearest metre.