The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun’s altitude is 30° than when it was 45°. Prove that the height of tower is metres.

Question

The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun&#x2019;s altitude is 30&#xB0; than when it was 45&#xB0;. Prove that the height of tower is metres.

Philoid · Accepted Answer

Let the height of tower is AB = h (m.)

Now in ∆ABD

tan 45° =

1 =

h = ------(1)

Now in ∆ABC

tan 30° =

=

√3h = 2 -------(2)

On substituting value of y from eqn. (1) in eqn. (2)

√3h = 2

√3h-h = 2

h (√3-1) = 2

h =

on rationalsing above fraction we get,

h =

Therefore height of tower is m.