A town Q is on a bearing of 210 degree from p,r is another on a Bearing of 150 degree from P is cast Q. The distance between R and P is 100m, find the distance between R and Q.
do we know PQ?
and 100m is not much distance between towns.
No response
Solution
Thanks
Solution
To find the distance between R and Q, we can use the concept of bearings and the given information.
First, let's draw a diagram to visualize the situation described in the question.
```
P
|
150° | 210°
---------Q---------
|
100m
|
R
```
In this diagram, P represents the starting point, Q represents the town located on a bearing of 210 degrees from P, and R represents the town located on a bearing of 150 degrees from P.
Now, let's break down the problem into two simpler right-angled triangles:
△PQR - Right triangle with hypotenuse PR and angle PQR.
△PQ'Q - Right triangle with hypotenuse PQ and angle PQ'Q.
Based on the information given, we know that angle PQR is 180° - 150° = 30° (interior angles of a triangle add up to 180°).
Furthermore, angle PQ'Q is 180° - 210° = -30° (since bearings are measured clockwise from the north).
Given that the distance between P and R is 100m, we need to find the distance between R and Q.
To solve this problem, we can use the trigonometric relationship of the tangent function:
tan(angle) = opposite/adjacent
In triangle △PQR:
tan(30°) = RQ / PR
Rearranging the equation to solve for RQ:
RQ = tan(30°) * PR
Substituting the given length of PR = 100m into the equation:
RQ = tan(30°) * 100m
Using a calculator, we can find the tangent of 30° (approximately 0.577):
RQ ≈ 0.577 * 100m
RQ ≈ 57.7m
Therefore, the distance between R and Q is approximately 57.7 meters.