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.

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- Nov 22nd 2006, 04:08 AMSohailbearing
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.

- Nov 22nd 2006, 05:25 AMearboth
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