Question

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 x ($\sqrt{3}+1$) metres.

Answer 1

Let AB be the tower of height h m. the length of shadow of tower to be found 2x meters at the plane longer when sun’s altitude is 30° than when it was 45°. Let BC = y m,
CD = 2x m and ,

We have to find the height of the tower

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle,

Again in a triangle

Hence the height of tower is m.