Question

The angle of elevation of the top of the tower from a point on the ground is found to be 45o. By going 50 m further
away from the tower, it is found to be 30o. Find the height of the tower

Answer 1

Let the Height of the tower be h

and Distance from base of the tower to the point be x

★Case 1:

• Angle of elevation of top of the tower from ground is 45⁰

→ tan 45⁰ = h/x

→ 1 = h/x

→ x = h [1]

★Case 2:

• By Going 50m Further away from the tower, angle of elevation will be 30⁰

→ tan 30⁰ = h/(x + 50)

→ 1/√3 = h/(x + 50)

→ x+50 = √3h

→ h + 50 = √3h

→ 50 = h(√3–1)

→ 50 = 0.72h

→ h = 70m

Hence,

The Height of the tower is 70 metres [approx.].