Q1: a point Pis 12 kilometers due north of another point Q.The bearing of a lighthouse, R, from P is 135 and, fro Q, it is 120. calculate the distance of PR.
Hello, Sohail,
1. Draw a sketch of the described situation (see attachment)
2. Bearings are measured from the North clockwise. So N = 0°, E = 90° etc.
3. You have a triangle QPR. You know all three angles and one leg. So use Sine rule to calculate the line PR:
4. $\displaystyle \angle(QPR) = 45^\circ$
$\displaystyle \angle(RQP) = 120^\circ$
$\displaystyle \angle(PRQ) = 15^\circ$
5. Use Sine rule:
$\displaystyle \frac{PR}{12\ km}=\frac{\sin(120^\circ)}{\sin(15^\circ)}$. Solve for PR.
I've got: $\displaystyle PR\approx 40.15\ km$
EB