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Pre – Calculus 20
Unit 3: The Law of Sines and Cosines
Review Assignment
Exam: Wednesday, October 24
THIS IS THE KEY TO MY SUCCESS! I WILL FINISH IT!!
1. Solve the triangles completely. Round angles to the nearest degree and the sides to the
nearest tenth.
a)
P
15
39°
Q
22
R
b)
D
145
28

110°
E
c)
C
43°
72°
A
30
B
F
2. Fred is supposed to construct a triangle with sides of 14 cm, 20 cm, and 24 cm. What
should the measure of the smallest angle of his triangle be to the nearest degree?
3. For ∆ABC if a = 14, b = 18, and A = 35o. Determine how many solutions are possible.
4. For ∆ABC if a = 9, b = 13, and A = 47o. Determine how many solutions are possible.
5. For ∆BAT if a = 15, b = 9, and A = 120o. Determine how many solutions are possible.
6. For ∆CAT if a = 11, c = 11, and C = 20o. Determine how many solutions are possible.
7. Determine if the information given on the sketch of the triangle actually gives one, two,
or no triangles and solve the triangle(s). Don’t let the diagram mislead you!
8. Determine side c if you are given ∆ABC with a = 7, b = 6, and C = 24o.
9. Determine side c in ∆ABC if B = 105o, b = 11, and a = 5.
10. Solve ∆ABC if a = 10, b = 18 and A = 35°.
For the following problems, make sure to include a labelled diagram, a LET statement,
and a sentence stating your answer.
11. In travelling to Jasper from Edmonton, you notice a mountain directly in front of you.
The angle of elevation to the peak is 4.1o. When you are 21 km closer to the mountain,
the angle of elevation is 8.7o. Determine the approximate height of the mountain to the
nearest metre?
12. Two planes take off from the same point. One plane is traveling N15°W and the other
N22°E. At a certain time the first plane has traveled 81 km and the second 72 km. How
far apart are the planes at that time?
13. A passenger jet is at cruising altitude heading east at 720 km/h. The pilot, wishing to
avoid a thunderstorm, changes course by heading N70oE. The plane travels in this
direction for 1 hour, and then turns toward his original flight path. He travels for 30
minutes in order to get to the original path.
a) What heading, east of south, did the plane take, after avoiding the storm, to head back
toward the original flight path?
b) At what distance, east of the point where it changed course, did the jet resume its
original path?
14. A tower standing on the top of a hill, that is inclined at an angle of 18°, casts a shadow 45
m long down the hill. The angle of elevation of the sun is 47°. What is the height of the
tower?
15. The 12th hole at a golf course is a 375-yd straightaway par 4. When Darla tees off, the
ball travels 20o to the left of the line from the tee to the hole. The ball stops 240 yd from
the tee. Determine how far the ball is from the centre of the hole.
16. Tracking station A is 20 km due west from Tracking station B. The two stations are
tracking a rocket, which is in between the two stations. The angle of elevation of the
rocket from A is 42o and from B, 78o. Find the height of the rocket in kilometres.
17. From the top of a house 15 m high, the angle of elevation to the top of pole across the
street is 9°. From the base of the house, the angle of elevation to top of the same pole is
42°. Find the height of the pole.
18. Two boats leave a dock at the same time. Each travels in a straight line but in different
directions. The angle between their courses measures 54o. One boat travels at 48 km/h
and the other travels at 53.6 km/h. How far apart are the two boats after 4 hours?
19. The sides of a parallelogram are 4 cm and 6 cm in length. One angle of the parallelogram
is 58o and a second angle is 122o. Determine the lengths of the two diagonals of the
parallelogram.