BC Learning Network – AW Math 10
Unit 7 – Trigonometry
Instructions:
Using a pencil, complete the following questions as you work through the
related lessons. Show ALL work as it is explained in the lessons. Do your best
and ask your teacher if you do not understand any question. Remember you
can use the data file for questions in the assignment and on the quizzes.
Lesson 1 The Pythagorean Theorem
1. Find the length of the unknown side in the following right triangles to the
nearest 100th [Two decimal places]
E
11
7
F
D
2. Find the length of the unknown side in the following right triangles to the
nearest 100th [Two decimal places]
3. Which of the two triangles below is a right triangle? Show all work to support
you answer.
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4. Determine the value of x in the diagram below? Round answer to 2 decimal
places. Note: Diagram is not drawn to scale
5. A sun deck is in the shape of a regular hexagon shown below. Calculate the
area of the sun deck.
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6. Moira left her house and walked 3.5 km due west and then turned directly
due north and walked an additional 4.5 km. What is the straight line distance
between Moira and her house. (Hint: draw a diagram) (Round answers to 1
decimal place)
7. A baseball diamond is a square with sides of 90 feet. What is the
shortest distance, to the nearest tenth of a foot, between first base and
third base?
Lesson 2 The Trigonometric Ratios
8. a) Label the opposite side .
and adjacent side for angle a
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b) Label the opposite side
and adjacent side for angle b
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9. Use this triangle for parts a
and b.
a) Write the sine, cosine and tangent ratios for angle A
b) Write the sine, cosine and tangent ratios for angle B
Lesson 3 The Sine Ratio
10. Find a
11. A six-meter-long ladder leans against a building. If the ladder makes an angle
of 60° with the ground, how far up the wall does the ladder reach?
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12. A five meter ladder is leaning against a wall. The top of the ladder reaches
four meters up the wall. What is the approximate angle that the ladder
makes with the ground?
13. If the safety information indicates the ladder should not be set up at an angle
greater than 750 or less than 450, what range of height can a 25foot ladder
reach?
Lesson 4 The Cosine Ratio
14. Find a
15. Find the size of angle X. (diagram not to scale)
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16. In the right triangle ABC, angle A = 340 and AB = 48.26. Find AC and CB to the
nearest hundredth.
Lesson 5 The Tangent Ratio
17. Find x
18. Find 

19. Find 

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20. A plane ascends at a 40° angle. When it reaches an altitude of one hundred
meters, how much ground distance has it covered?
21. From a horizontal distance of 80.0 m, the angle of elevation to the top of a
flagpole is 180. Calculate the height of the flagpole to the nearest tenth of a
metre.
22. A tower, 28.4 feet high, must be secured with a guy wire anchored 5 feet from
the base of the tower. What angle will the guy wire make with the ground?
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23. When the foot of a ladder is 2 m from the base of a wall, the angle formed by
the ladder and the ground is 680. (draw a diagram)
a) How high up the wall does the ladder reach?
b) How long is the ladder?
24. Shawn is standing on a surveyor’s mark and he measures the angle of
elevation to the top of a tower is 320 and the tower is 450 feet high . If the
Shawn and the tower are on level ground how far away is Shawn from the
base of the tower? (draw a diagram).
25. A jetliner is flying at 35 000 feet above the ocean. The pilot spots an island
and measures the angle of depression to the coast of the island to be 5 .
Determine the horizontal distance in miles from the jetliner to the coast of
the island.
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Answers:
1.
2.
3.
4.
5.
6.
7.
8.
8.49
7.21
triangle A
18.03
6120 cm2
5.7 km
127.3 ft
a)
b)
12
13
5
9. a) cosA 
13
12
tan A 
5
5
13
12
b) cosB 
13
5
tan B 
12
sin A 

10. 3.54
11. 5.2
12. 530
13. 17.7’ to 24.1’
14. 6.93
15. 22.62
16. BC = 26.99 AC = 40.01
17. 25.52
18. 11.30
19. 590
20. 119.18 m
21. 25.99 m
22. 800
23. a) 5 m b)5.3 m
24. 720.2 ft
25. 75.8 mi
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sin B 

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