From the top of a tower the angle of depression of an object on the horizontal ground is found to be 60degree. On descending 20 m vertically downwards from the top of the tower, the angle of depression of the object is found to be 30degree Find the height of the tower.

Answer 1

make your sketch
label the top of the tower A, bottom of tower B,
object on ground C and the point 20 m from the top as D
in triangle ACD
angle ACD = 60° - 35° = 25°
angle A = 180° - 90° - 60° = 30°
and AD = 20
by the sine law
CD/sin30 = 20/sin25
CD = 20sin30/sin25

in the right-angled triangle DCB
sin35 = DB/CD
DB = CDsin35
= 20sin30 sin35/sin25 , notice I have not yet touched my calculator , now I will
= 13.57

so the height of the tower is 20+13.57 = 33.57 m

Answer 2

good work, but - where did the 35° come from?

Answer 3

Rats!!

Just have to get better glasses, I read the 30° as 35°

Just how do you spot those little typos? Amazing.