Precalculus Honors
Name:
4.5d: Law of Sines and Cosines Word Problems
Date:
Per:
1. A boat travels at a speed of 30 mph from its home port with a bearing of 95˚ for two hours and then
changes to a bearing of 185˚ for two hours traveling at the same speed. Determine the distance from the
boat to its home port and the bearing from the home port to the boat.
2. Boats A and B leave from ports on opposite sides of a large lake. The ports are on a due east-west line.
Boat A steers a bearing of 105˚ and boat B steers a bearing of 195˚. Boat A averages 23 mph and collides
with boat B (it was a foggy night…ouch). What was boat B’s average speed?
3. A forest ranger at an observation point A along a straight road sights a fire in the direction N32˚E.
Another ranger at a second observation point B on the road, 10 miles due east of A, sights the same fire at
N48˚W. Determine the distance from each observation point to the fire, and determine the shortest
distance from the road to the fire.
Precalculus Honors
Name:
4.5d: Law of Sines and Cosines Word Problems
Date:
Per:
4. In major league baseball, the four bases form a square with sides of length 90 feet. The front edge of
the pitching rubber is 60.5 feet from home plate (hint- the pitching mound is on the segment from home
plate to second base). Determine the distance from the front of the pitching rubber to first base.
5. The lid on a grand piano is held open by a prop 28 inches long. The base of the prop is 55 inches from
the lid’s hinges. At what possible distances along the lid could you place the end of the prop so that the
lid makes an angle of 26˚ with the piano?
6. From one corner of a triangular plot of land, a surveyor determines the directions to the two other
corners to be N32˚E to point A and S76˚E to point B. What is the measure of the angle formed by the
edges of the plot of land at the corner where the surveyor is standing? If the distance from the surveyor to
point A is 150 ft and the distance from the surveyor to point B 210 ft, how far apart are point A and B and
what is the area of the plot of land?
Precalculus Honors
Name:
4.5d: Law of Sines and Cosines Word Problems
Date:
Per:
7. Two hikers follow a trail that splits into two forks. Each hiker takes a different fork. The forks diverge
at an angle of 67˚ and both hikers walk at a speed of 3.5 mi/h. How far apart are the hikers after one hour?
8. After leaving an airport, a plane flies for 1.5 h at a speed of 200 km/h on a bearing of 200˚. Then, on a
bearing of 340˚, the plane flies for 2h at a speed of 250km/h. At this time, how far from the airport is the
plane?
9. Two planes take off from an airport at 9:15 am. One flies on a bearing of 86˚ at a constant rate of 190
mi/h. The second one flies on a bearing of 176˚ at 160 mi/h. How far apart are they at 10:45 am?