Question

From the top of a hill, in east side at two points angle of depressions are 30° and 45°. If distance between two points is 1 km, then find height of the hill.

Answer 1

Let height of hill AB is h km. In the east side of hill there are two points C and D respectively.

The angle of depression are 30° and 45°. 

The distance between CD = 1 km.

Let AC = x km

From right angled ΔACB

tan 45° = AB/AC

⇒ 1 = h/x

⇒ h = x

From right angled ΔDAB,

tan 30° = AB/AD

⇒ 1/√3 = h/(x + 1)

⇒ √3h = x + 1

Put the value of x from equation (i) in equation (ii)

√3h = h + 1

√3h – h = 1

h(√3 – 1) = 1

h = 1/(√3 - 1) = 1/(1.732 - 1)

=  1/0.732

= 1.366 km

Hence, height of hill = 1.366 km