Precalculus Honors Name____________________________

Chapter 9 Practice Problems Date_____________________________

1. A boat travels at a speed of 30 mph from its home port on a course of 95˚ for two hours and then

changes to a course 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 course of 105˚ and boat B steers a course 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____________________________

Chapter 9 Practice Problems Date_____________________________

4. In major league baseball (Go Yankees!), 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. 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____________________________

Chapter 9 Practice Problems Date_____________________________

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 course of 200˚. Then,

on a course of 340˚, the plane flies for 2h at a speed of 250km/h. At this time, how far from the

airport is the plane? If the plane wanted to return to the airport, what bearing must it fly at?

9. Two planes take off from an airport at 9:15 am. One flies on a course of 86˚ at a constant rate of

190 mi/h. The second one flies on a course of 176˚ at 160 mi/h. How far apart are they at 10:45

am and what are each of their bearings?

10. A jet flew 140 miles on a course of 196˚ and then 120 miles on a course of 106˚. Then the jet

returned to its starting point via the shortest route possible. Find the total distance that the jet

traveled.