Question

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

Answer 1

1. 
   
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