Question

A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30km on a bearing of 210° from C.  

1. Using a scale of 1:500,000, represent the above information on a scale drawing
2. Using the scale drawing, determine the:  
   • distance, in kilometres, of D from A: 
   • bearing of A from D 
3. Calculate the area, correct to 1 decimal place, of the forest in square kilometres.

Answer 1

1. ​​​​​​ 
    
2. AD=8.7cm × 5km
   1cm
   = 43.5km ± 0.5
   bearing of A from D is 048° or N48°E
    
3. A∆ABC =½ × 21 × 25 sin 45°
    = 185.62 km²

A∆ACD = ½ ×30 × 43.5 sin 18°
          =201.63km²

total area= 185.62 + 201.63
              = 387.25km²
              ≈ 387.3km²