Math 10H
Name: ________________
Unit 7: Trigonometry Review Package
These are the trig-related formulae that you will see on your provincial exam:
These are the additional formulae I will provide for your Honours unit exam:
Sine Law:
sin A sin B sin C


a
b
c
(ASA or AAS)
Cosine Law:
a 2  b 2  c2  2bccos A
(SSS or SAS)
45
60
2
2
1
1
45
1
30
3
Math 10H
1.
Name: ________________
Determine the measure of BCD . Answer to the nearest degree.
1. ________
2.
Determine the length of x . Answer to the nearest tenth.
2. ________
3.
Determine the length of x . Answer to the nearest tenth.
3. ________
Math 10H
4.
Name: ________________
Determine the measure of PSR . Answer to the nearest degree.
4. _________
5.
What obtuse angle has a sine value of
2
? Answer to the nearest tenth of a degree.
5
5. _________
6.
Determine the length of side PQ. Round to two decimal places.
6. _________
7.
To display a valuable specimen of moon rock, staff at the Space Centre roped off a
triangular area and installed a security camera, as shown below.
The security camera was installed so that it scanned continually between the two
longest ropes through the angle C. Determine the measure of C . Answer to the
nearest degree.
7. _________
Math 10H
8.
Name: ________________
Given that the area of any triangle can be determined with the formula:
1
A  bcsin A , determine the area of the triangle shown below. Answer to the
2
nearest m 2 .
8. __________
9.
Determine the measure of A , to the nearest degree, if 0  A  90 and
cos125   cosA .
9. _________
10. Solve for x . Round your answer to the nearest hundredth.
10. _________
Math 10H
Name: ________________
11. From where she parked her car, Jade observed that the angle of elevation to the top
of a building was 25 . When she walked 50 m closer to the building, the angle of
elevation became 60 . Determine the distance from the base of the building to her
car. Round the answer to the nearest hundredth metre.
11. _________
12. Determine the value(s) for A if sin A  0.5 and 0  A  180 .
12. _________
2
and  is an obtuse angle, what is the value of cos ? Round your
3
answer accurately to four decimal places.
13. If sin  
13. _________
14.
Calculate the length of YZ. Answer to nearest hundredth.
14. __________
15. Determine the length of QR to the nearest metre.
15. __________
Math 10H
Name: ________________
16. Determine the length of AB. Answer to nearest hundredth.
16. __________
17. Determine the measure of ADC . Answer to nearest degree.
17. __________
18. Determine the value of CAD . Answer to nearest degree.
18. __________
Math 10H
Name: ________________
19. Which of the following expressions has the same value as cos 180  X  , where
0  X  90 ?
A. cos X
B.  cos X
C. sin X
D.  sin 180  X 
20. Determine the length of side XY. Answer to nearest meter.
20. __________
21. Use the diagram below to determine a , where a 2  512  622  2(51)(62)cos 49 .
21. __________
22. Solve for x . Answer to nearest tenth.
22.
___________
Math 10H
Name: ________________
23. In ABC , C  90 , AB = 17 cm, and AC = 15 cm. Calculate the measure of
ABC to the nearest degree.
23. _________
24. A 10 metre tall farmhouse is located 28.0 m away from a tree with an eagle’s nest.
The angle of elevation from the roof of the farmhouse to the eagle’s nest is 30 .
What is the height of the eagle’s nest, to the nearest metre?
24. __________
25. Ann and Bryon positioned themselves 35 m apart on one side of a stream. Ann
measured the angles, as shown below.
Calculate the height of the cliff on the other side of the stream to the nearest tenth of
a metre.
25. __________
Math 10H
Name: ________________
26. A ramp is set up using a rectangular piece of plywood (shaded region) as shown
below.
Calculate the area of the plywood. Answer in square metres to one decimal place.
26. _________
27. a) Determine the ratio of cosA .
27. a) ________
b) Determine the value of A , to the nearest degree.
27. b) ________
28. The angle of elevation of the sun is 15 . How long is the shadow of a 64 m tall
building? Answer to nearest metre.
28. ________
29. As Tracey is driving, she sees a sign telling her the road has a 7% grade (ie., a rise
of 7 metres for a horizontal change of 100 m). Circle one of the following
expressions that will calculate the angle between the road and the horizontal.
 7 
A. tan 

 100 
 7 
B. sin 

 100 
 7 
C. tan 1 

 100 
 7 
D. sin 1 

 100 
Math 10H
Name: ________________
30. Mission’s outdoor club collected the following data to determine the height of a
cliff.
Calculate the height of the cliff. Answer to the nearest tenth of a metre.
30. __________
31. Calculate the length of side x on the diagram below. Answer to the nearest cm.
31. __________
Math 10H
Name: ________________
32. Remember the special triangles:
A right triangle with two sides of equal lengths is a 45- 45- 90 triangle.
a) Find the length of the hypotenuse of a right triangle if the lengths of the other
two sides are both 3 cm. Leave answer in exact radical form.
32. a) ________
b) In the diagram below, if BD bisects AC and AC = 10, what is the length of AB?
Leave answer in exact radical form.
32. b) _________
c) Find the lengths of the other two sides of a right triangle if the length of the
hypotenuse is 4 2 cm and one of the angles is measured to be 45 .
32. c) _________
Math 10H
Name: ________________
33. Also remember:
A right triangle with angles 30- 60- 90 is also considered “special”.
a) Find the length of the hypotenuse of a right triangle if the lengths of the other
two sides are 4 cm and 4 3 cm.
33. a) _________
b) Find the lengths of the other two sides of a right triangle if the length of the
hypotenuse is 14 cm and one of the angles is measured to be 30 .
Leave answers in exact radical form if necessary.
33. b) _________
34. At 9:00 AM, ship C leaves port traveling at 30 km/hr on a bearing of 63 . At the
same time, ship B leaves port on a bearing of 315 at a speed of 19 km/hr. When
the boats stop after two hours,
a) how far east is ship C at point C?
b) what is the angle between their paths?
c) how far apart are the boats after 2 hours? (hint – use Cosine Law)
y
North
(0o)
C
B
315o
63o
x
South
(180o)
Math 10H
Name: ________________
Solutions to Unit 7: Trigonometry Review Package
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
118
34.8 cm
94.8
52
156.4
21.34 cm
42
5879 m 2
55
5.17
68.42 m
30 and 150
-0.7454
19.61 cm
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
63 m
28.96 cm
114
74
B
69 m
48 cm
12.8
62
26 m
107.1 m
10.2 m 2
5
a)
3
b) 42
28.
29.
30.
31.
32.
33.
34.
239 m
C
26.1 m
45 cm
a) 3 2 cm
b) 5 2
c) 4 cm, 4 cm
a) 8 cm
b) 7 cm, 7 3 cm
a) 53.46 km
b) 108
c) 80.33 km
26.1