Question

from the top of a 300m height light house ,angle of depression of the top and foot of a tower have measured 30 and 60 . find the height of the tower.

Answer 1

May this will help you

Answer 2

Hey friend,

Refer to the attached diagram...

tanA = perpendicular / base

In triangle CBD,
tan 60 = CD / BD
$\sqrt{3}$ = 300 / BD
BD = 100 x $\sqrt{3}$ 

In triangle ACE,
tan30 = CE / AE     [AE = BD]
1 / $\sqrt{3}$ = CE / 100 x $\sqrt{3}$ 
CE = 100 m

Therefore,
CD - CE = DE
DE = 300 - 100
DE = 200 m   [DE = AB]
AB = 200 m

Therefore, the height of the tower is 200 m.

Hope it helps!