Question
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
?
120 km on a bearing of
drove for another 100 km on a bearing
of
(a) What is the distance between the
(b) Wan’s office and the town?
(b) is the bearing of
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.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
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
.
(a) Approximately
(b) Bearing of