Question

From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30 and 60 respectively. What is the height of the pole?

Answer 1

Let the distance between foot of hill & pole be 'a' and height of pole be 'h'.
tan 30 = (100 - h) / a
1 / sqrt3 = (100 - h) /a
a = sqrt3 * (100-h) ----------------- (1)
tan 60 = 100 / a
sqrt3 = 100 / a
a = 100 / sqrt3 ---------------------- (2)
Now equating (1) & (2),
100 / sqrt3 = sqrt3 * (100-h)
100 = 3*(100-h)
100 = 300 - 3h
3h = 300 - 100
h = 200/3
Height of pole = 200/3m ans