Question

when the sun altitude increases from 30 degrees to 60 degrees the length of Shadow of a tower decreases by 60 M find the the height of the tower​

Answer 1

Answer:

When sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70 m.

Formula used:

Tanθ = Perpendicular/Base

Tan60o = √3

Tan30o = 1/√3

Calcuation:

Let CD distance be X

In Δ ABC

⇒ Tan30o = h/(X + 70)

⇒ 1/√3 = h/(X + 70)

⇒ √3h = X + 70 ----(1)

In Δ ADC

⇒ Tan60o = h/X

⇒ √3 = h/X

⇒ X = h/√3

Putting X in equation (1)

⇒ √3h = h/√3 + 70

⇒ 2h = 70√3

⇒ h = 60.6 m

∴ The height of the tower is 60.6 m.