### Bearings word problems KEY

```Advanced Alg & Trig
WS Bearings
Name
Date
{.n,,,,
Period
Draw a picture. w-rite an equation, and then solve the problem using bearings and trigonometry.
Ouestions (1-6)
i)
A ship is 9 rniles
*
Pythagorean Theorem and Basic Trig Ratios (SOHCAHTOA)
east and 6 miles south of a
harbor. What bearing should be taken to sail
directly to the harbor?
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2)
A boat leaves the entranc" io u harbor and travels 150 miles on a bearing of N 53" E.
How many miles rlorth and how many miles east from the harbor has the boat traveledJ
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3)
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A lbrest ranger sights a fire directly to the south. A second ranger, 7 miles east oTthe first
ranger, also sights the fire. The bearing from the second ranger to the fire is S 28"W.
How far, to the nearest tenth of a mile, is the first ranger ffithe fire?
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7
A boat leaves the entrance to a harbor and travels 40 miles on a bearing of S 64"E. How
many miles south and how many miles east from the harbor has the boat traveled?
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**5)
A jet leaves a runway whose bearing is N 35"E from the control tower. After flying 5
miles, the jet turns 90o and flies on a bearing of q 55"E for 7 miles. At that time, what is the
bearing of the jet from the control tower?
6)
A ship is due west of a lighthouse. A second ship is 12 miles south of the first ship. The
bearing fiom the second ship to the lighthouse is N 64'E. How far, to the nearest tenth of
mile, is the first ship fprdthe lighthouse?
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Questions (7- 10) * Law of Cosines and Law of Sines
7)
Two ships leave a port at the same time. Ship A heads N43"E, and Ship B leaves heading
522F,. When Ship A rs 432 miles from the port, and Ship B is 375 miles from the port,
how lar away arelhe two ships from each other?
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8)
A ship leaves a
heading N43"E. After 143 miles, the ship turns and heads due east
for another 96 miles. I{ow.far has the ship sailed from the harbor?
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e)
Two trains leave a station at the same time. Train A heads S16"E while the Train B heads
N71'W. After 2 houts, Train A is 175 miles from the station. and Train B is 214 miles
from the station. How far apart are the trains from each other?
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^41
A plane leaves an airport at a bearing of N54'W. It stops in Awesomeville before heading
due west to its 1-rnal destination, Cool Town. From the airport to Awesomeville, the plane
traveled 376 miles. From Awesomeville to Cool Town, the plane flew another 238 miles.
What would the distance have been if the plane had taken a direct path? What is the
difference between routes? '
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