Question

The angle of elevation of the top of an unfinished tower from a point at a distance of 80 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?

Answer 1

Let AB be the unfinished tower and C be the top of the tower when finished, Let P be a point 80 m from the foot A.

In ΔBAP, 

`tan 30^circ = (AB)/(AP)`

`=> 1/sqrt(3) = (AB)/(80)`

`=> AB  = 80/sqrt(3) = 46.19  m`

In ΔCAP,

`tan 60^circ = (AC)/(AP)`

`=> sqrt(3) = (AC)/(80)`

`=> AC = 80sqrt(3) = 138.56  m`

Therefore, the tower must be raised by (138.56 – 46.19) m = 92.37 m