Pre-Calculus
Name ________________________
LAW OF SINES/COSINES – word problems
Classwork:
1) A plane leaves Kittredgeville at a bearing of S24°E and flies at a speed of 400 mph for 2.5 hours. Over Norwood
Town, the plane turns at a bearing of S80°E and continues for another 1.5 hours.
a) Draw a picture of this situation.
b) How far is the plane from the starting point?
c) Through what angle would the pilot turn in order to head back to Kittredgeville?
d) What is the bearing from the current location (after the 4 hours of flying) back to Kittredgeville?
2) Ava is in the smaller building looking out of a window. She sights the top of the taller building at an angle of
elevation of 40. She sights the bottom of the taller building with an angle of depression of 20. If the building is 200
feet tall, how high up is she in the smaller building? How far apart are the two buildings?
3) A triangle has the given information: a = 2, b = 3, A = 20°.
Find the area of the triangle. If two triangle are possible, find the area of both triangles.
Pre-Calculus
LAW OF SINES/COSINES – word problems HW#72
Name ________________________
1. Two radar stations are tracking the same plane. The angle of elevation from Station A to the plane is 67°, the angle
of elevation to the plane from Station B is 82. Station A is .7 miles from Station B. Find the altitude of the plane.
Station A
Station B
3. Find the measure(s) of A in each triangle:
A
a)
b) a = 20, b = 15, B=42
24
30
c) mC = 31, a = 16, c = 8
40
4. Find the area of the quadrilateral.
12.6 cm
46°
8 cm
7.2 cm
42°
8.6 cm
5. Spencer is taking a flight from Phoenix, AZ to San Francisco. There is a stopover in Las Vegas, NV. The bearing
from Phoenix to Las Vegas is N42W. The bearing from Las Vegas to San Francisco is N71W. The distance of the
first leg of the trip from Phoenix to Las Vegas is approximately 259 mi. From Las Vegas to San Francisco is another
413 mi. *All measurements here are approximate, but pretty close!*
a) A direct flight from Phoenix to San Francisco without a stopover would be shorter; how much shorter?
b) What is the bearing from Phoenix to SF?
SF
LV
PHX
6. Two ships leave a harbor at the same time. One ship travels at a bearing of S12°W at 14 mph. The other ship travels
on a bearing of N75°E at 10 mph. How far apart will the ship be after three hours?
H
7. Closed to tourists since 1990, the Leaning Tower of Pisa in Italy leans at an angle of about 84.7°. The figure shows
that 171 feet from the base of the tower, the angle of elevation to the top is 50°. If a bird is sitting on the very top of the
tower, how high is the bird?
50°
171 ft
8. You are on a fishing boat that leaves its pier and heads east. After traveling for 30 miles, there is a report warning of
rough seas directly south. The captain turns the boat and follows a bearing of S45°W for 12 miles.
a) At this time, how far are you from the boat’s pier?
b) What bearing could the boat have originally taken to arrive at this spot?
c) What is the angle that the boat had to turn after the 12 miles to head back to the pier?
Optional: Do on a separate piece of paper.
7
q
(in quad IV) find cos .
2
2


 2
1
11. Find the exact value of cos sin 1 
  sec ( 2) 


 3 
9. Given that secq =
10. Find the exact value of: csc(2tan -1 3)
 11 

 12 
12. Find the exact value of tan 
Solve in the interval 0,2  . Leave answers exact when possible otherwise round to the hundredth.
13. cosq = -.8
14. cscq + cot 2 q =1
Establish the identity.
sin 
17. csc   cot  
1  cos 
15. tan 2q = - 3
18.
1  csc 
 sec 
cos   cot 
2
16. cos 2  2sin 