Question

The angle of elevation from a point P of the top of a tower QR, 50 m high is 60°, and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest meter.

Answer 1

In ΔPQR

`tan 60^@ = (RQ)/(PQ)`

`sqrt3 = 50/(PQ)`

`PQ = 50/sqrt3`

In ΔPQT

`tan 30^@ = (PT)/(PQ)`

PT = PQ × `1/sqrt3`

PT = `1/sqrt3 xx 50/sqrt3` 

= `50/3`

= 16.67 m