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Practice Questions: Trigonometric Ratios
1. Answer the following questions using the diagram below:
a) Find the measure of side a to the nearest centimetre.
b) Find the measure of side c to the nearest centimetre.
c) Find the measure of angle A.
A
25 cm
c
25'
B
a
2. Answer the following questions using the diagram below:
a) Find the measure of angle A to the nearest degree.
b) Find the measure of angle B to the nearest degree.
c) Find the measure of side b to the nearest centimetre.
10 cm
A
36 cm
B
3. Answer the following questions using the diagram below:
a) Find the measure of side a.
b) Find the measure of the hypotenuse.
A
66'
5.5 m
B
4. Answer the following questions using the diagram below:
a) Find the measure of side b.
b) Find the measure of side c.
A
70'
C
B
35.5 cm
5. Answer the following questions using the diagram below:
a) Find the measure of angle B.
b) Find the measure of the hypotenuse.
A
65 m
C
B
100 m
6. An airplane is coming down for landing at Pearson Airport.
The plane is at a 22 degree downward approach angle, and
350 metres from the landing point along the ground.
How high is the plane?
350 m
7. You are playing paintball with friends and are lying on the
ground scanning for “enemies”. You look up at an angle of
55 degrees and see that your friend is in a tree 30 metres
ground travel away from you.
How high up in the tree are they?
Draw the diagram yourself, then solve.
Word Problems: using primary trig ratios
1. An archer shoots and gets a bulls-eye on the target. From the archer’s
eye level the angle of depression to the bulls-eye is 5°. The arrow is in the
target 50 cm below the archer’s eye level. Calculate the distance the
arrow flew to hit the target (the dotted line).
C
5°
B
50 cm
A
2. A sailboat that is 2 km due west of a lighthouse sends a signal to the
lighthouse that it is in distress. The lighthouse quickly signals a rescue
plane that is 7 km due south of the lighthouse. What heading from due
north should the plane take in order to intercept the troubled sailboat?
2 km
B
C
7 km
A
3. While walking to school you pass a barn with a silo (???). Looking up to
the top of the silo you estimate the angle of elevation to the top of the silo
to be about 14°. You continue walking and find that you were around
40 m from the silo. Using this information and your knowledge of
trigonometric ratios, calculate the height of the silo.
A
14°
B
40 m
C
4. A sailboat is approaching a cliff. The angle of elevation from the sailboat
to the top of the cliff is 35°. The height of the cliff is known to be about
2000 m. How far is the sailboat away from the base of the cliff?
A
2000 m
35°
C
B
5. You’re out in a field flying your kite. You have just let out all 150 m of your kite
string. You estimate that the kite is at an angle of elevation from you of about
20°. Can you calculate the height of your kite above the ground?
6. A golfer hit her tee shot so that it landed about 7 metres behind a 40 metre
tall pine tree as shown. She decided to take her second shot and hoped
the ball would make it over the top of the tree. She used her lob wedge
and hit the ball, sending it upward at an angle of 60. Was she able to
clear the top of the tree?
7. Challenge: Draw a diagram to solve the problem.
A search and rescue helicopter is flying at an altitude of 600m. A campfire is
spotted at an angle of depression of 15.2.
(0 depression is a level helicopter, flying parallel to the ground. The greater the
depression, the more tilted towards the ground the helicopter is)
0 depression
small degree of depression
large degree of depression
What is the exact distance between the helicopter and the campfire?
For the following questions you will need to create your own diagrams.
Draw them carefully and refer to the written description for clues!
8.
Two islands A and B are 3 km apart. A third island C is located due south
of A and due west of B. From island B the angle between islands A and
C is 33°. Calculate how far island C is from island A and from island B.
9.
The foot (bottom) of a ladder is placed 1.5 m from a wall. The ladder
makes a 70° angle with the level ground. Find the length of the ladder.
(Round to one decimal place.)
10.
A tow truck raises the front end of a car 0.75 m above the ground. If the
car is 2.8 m long what angle does the car make with the ground?
11.
A construction engineer determines that a straight road must rise vertically
45 m over a 250 m distance measured along the surface of the road (this
represents the hypotenuse of the right triangle). Calculate the angle of
elevation of the road.