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  1. #1
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    bearing

    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.
    Last edited by Sohail; November 22nd 2006 at 04:30 AM.
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  2. #2
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    Quote Originally Posted by Sohail View Post
    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. \angle(QPR) = 45^\circ
    \angle(RQP) = 120^\circ
    \angle(PRQ) = 15^\circ

    5. Use Sine rule:
    \frac{PR}{12\ km}=\frac{\sin(120^\circ)}{\sin(15^\circ)}. Solve for PR.

    I've got: PR\approx 40.15\ km

    EB
    Attached Thumbnails Attached Thumbnails bearing-peilung_leuchtturm.gif  
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