Question

The angle of elevation of the top of a tree from a point P on horizontal ground is 30º. From another point Q 8 metres from the base of the tree, the angle of elevation of the top of the tree is 48º.

1. Calculate to one decimal place the height of the tree.
2. Calculate the distance between P and Q 

Answer 1

1. 
   
   Tan 48 = ^h/₈
          h = 8 tan 48 =8.885
2. Tan 30 = 8.885                   
                   PF
         PF = 8.885 = 15.39
                  tan30
        PQ = 15.39 − 8 =7.389