____ Name: _________________________
45
Unit 1: Trigonometry Assignment
Unit Goals:
I will be able to….
· Determine the angle of a right triangle given 2 sides using SOHCAHTOA
· Determine the side of a right triangle given one side and one acute angle using Pythagorean Theorem or SOHCAHTOA
· Determine the obtuse value of an angle using the C.A.S.T rule
· Determine the angle or unknown side using Sine Law
· Determine the angle or unknown side using Cosine Law.
Mark
_________
XXXXXXXXXX
Part A: Multiple Choice – write your answer as a capital on the small left line ( marks)
____ 1. Which primary trigonometric ratio can you use to calculate the length of side q?
a.
tan 51°
b.
sin 51°
c.
sin 90°
d.
cos 51°
____ 2. Determine the length of side g, give the angle of 51 degrees and the side length of 94m.
a.
149 m
b.
94 m
c.
51 m
d.
116 m
____ 3. A pilot must fly 23.0 km before she is over the ocean.
The angle of depression to the ocean shoreline is 28°.
What is the pilot’s altitude?
a.
About 20.3
b.
About 43.3
c.
About 26
d.
About 12.2
_____ 4 . Marc is building a wheelchair ramp for the front door of his house. The ramp needs to have a vertical rise of 75 cm over a horizontal distance of 120 cm. At what angle of elevation should he build the ramp to the nearest degree?
a.
39
c.
51
b.
58
d.
32
____ 5. A surveyor takes measurements of a cliff using a laser range finder.
He measures 31.8 m to the top of the cliff, and an angle of elevation of 61°.
How high is the cliff?
a.
About 7.5 m
b.
About 65.6 m
c.
About 15.4 m
d.
About 27.8 m
____ 6. Choose the angle that has a negative cosine value
a.
332 degrees
c.
12 degrees
b.
72 degrees
d.
137 degrees
____ 7. Rhonda is on the roof of her apartment building. The apartment building across the
street is 15.5 m away. The angle of depression to the ground from the top of the other building is 50. How tall is the apartment building, rounded to the nearest tenth of a metre?
a.
20.2 m
c.
10.0 m
b.
24.1 m
d.
13.0 m
____ 8. George is flying a kite. The kite is directly over a picnic table which is 5 m away from George. The angle of elevation of the kite is 42. What is the distance between George and the kite, rounded to the nearest tenth of a metre?
a.
6.7 m
c.
5.6 m
b.
7.5 m
d.
3.7 m
____ 9. Adele is bird-watching. She spots a bald eagle in the sky and determines that it is
a distance of 4.2 km from her position on the ground. The angle of elevation is 39. How high above the ground is the eagle, rounded to the nearest tenth of a kilometre?
a.
3.3 km
c.
3.4 km
b.
2.6 km
d.
6.7 km
____ 10. The terminal arm of an angle, θ, in standard position passes through P(3, 5). Determine the length of OP to three decimal places.
a.
5.831
c.
6.931
b.
6.381
d.
7.481
Part B: – show all your work!!
1. For each of the following trigonometric ratios, state the acute and principle angles XXXXXXXXXXmarks)
a) Sin A = 0.3495 ∠ A = _____________________
) Cos B = XXXXXXXXXX ∠ B = _____________________
c) Tan C = XXXXXXXXXX ∠ C = _____________________
2. State the equivalent principle angle of both [ 2 marks]
a] sin 37° _________________ XXXXXXXXXXb) Tan 37°________________
3. A
idge across a valley is 137 m in length. The valley walls make angles of 60º and 54º with the
idge that spans it, as shown. How deep is the valley? [6 marks]
Hint: The depth or altitude of the triangle is not at the midpoint of the
idge, therefore you can’t cut 137 meters in half.
4. Determine the length of side u to one decimal place. (4 marks)
5. Calculate the value of
42°
6. The Skylon Tower in Niagara Falls is about 160 m high. From a certain distance, the angle of elevation is 65 degrees. If you walk backwards 20 m away from the tower, what is the new angle of elevation? [ 6marks]
XXXXXXXXXX. Two ranger stations are located in a pine forest and are 8 km apart. Label the stations A and B. A forest fire
eaks out at point F and is spotted by each of the rangers. The angle formed at station A by the line of sight to the fire and the line to station B is 61°. The angle at station B formed by the line of sight to the fire and the line between the ranger stations is 48°.
a) Which ranger is closer to the fire, and by how much? [ 7 marks]
XXXXXXXXXXFIRE
8. Two fe
ies leave dock B at the same time. One travels 2900 m on a bearing of 98°. The other fe
y travels 2450 m at a bearing of 132°. How far apart are the fe
ies? [ 5 marks]