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Four towns are situated in such a way that town Q is 500km on a bearing of 120º from P. Town R is 240km on a bearing of 210º from town P, while town S is due north of town Q and due east of town P.

  1. Draw a sketch diagram showing the relative positions of P, Q, R and S. 
  2. Find by calculation
    1. the distance QR
    2. the distance QS 
    3. the angle PRQ 
    4. area of triangle PQS

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  1. sketch diagram showing relative positions of PQR and S
  2.  
    1. QR=√(5002 + 2402)
          =554.7km
    2. Sin 30 = QS 
                    500
             QS =500 sin 30
                  =250km
    3. Tan PRQ =500 =2.083
                         240
         ∟PRQ =64.36°
    4. A = ½ × 500 × 250 sin 60
        = 54126.6km2

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