Question
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A man drove a car from his office ,
120 km on a bearing of , and then
drove for another 100 km on a bearing
of until he reached a town .
(a) What is the distance between the
(b) Wan’s office and the town?
(b) is the bearing of from ?

Ask by Ford Romero. in Nigeria
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The distance between the man’s office and the town is approximately 195.13 km. The bearing of the office from the town is approximately 228 degrees.

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Beyond the Answer

To find the distance between the man’s office and the town , we can use the Law of Cosines. First, we need to determine the angles involved. The angle at can be calculated by finding the angle between the two bearings:
The first bearing is and the second is . The interior angle at would be .
Using the Law of Cosines:
Calculating this gives .
Now, for the bearing of from , we need to calculate the angle counterclockwise from the north at point . The required angle can be obtained by subtracting the bearing from to to find its angle with respect to the north. The answer would be , hence the bearing of from is (which is ).
So, the final answers are:
(a) Approximately .
(b) Bearing of from is .

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