The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun’s elevation is 30° than when it was 45°. The height of the tower in metres is
In Δ DBC
tan 45° = h /y
h = y (∵ tan 45° = 1)……….1
In ΔACD
tan 30° =
=
√3 h = 2x + h (from 1)
2x= (√3- 1) h
h =
h = (√3 +1)x meter