Question

The angles of elevation of an artificial earth satellite, as measured from two earth stations are on the same side of it are 30°&60°.if the distance between the earth stations are 4000km, find the height of the satellite

Answer 1

Dear Student,

◆ Answer -

h = 3464 km

◆ Explanation -

Let h be height of satellite from earth.

Horizontal distance of satellite from 1st point is -

l1 = h/tanθ1

l1 = h/tan30°

Horizontal distance of satellite from 2nd point is -

l2 = h/tanθ2

l2 = h/tan60°

Distance between two points is given.

l1 - l2 = h/tan30° - h/tan60°

4000 = h (1/tan30° - 1/tan60°)

4000 = h (1/0.5773-1/1.732)

h = 4000 / 1.155

h = 3464 km

Hence, height of satellite is 3464 km.

Hope this helps you.