The length of the shadow of a tower standing on level ground 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 (√3+1)x
metres.

Question

The length of the shadow of a tower standing on level ground 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 (√3+1)x
metres

Manish Bharti · Accepted Answer

$I n Δ B C D, \tan 45^{0} = \frac{h}{y} \Rightarrow h = y ......... (1) I n Δ A B C, \tan 30^{0} = \frac{h}{2 x + y} \frac{1}{\sqrt{3}} = \frac{h}{2 x + y} 2 x + y = \sqrt{3} h 2 x + h = \sqrt{3} h (f r o m e q u . 1, y = h) 2 x = (\sqrt{3} - 1) h \Rightarrow h = \frac{2 x}{\sqrt{3} - 1} \times \frac{\sqrt{3} + 1}{\sqrt{3} + 1} \Rightarrow h = (\sqrt{3} + 1) x$

The length of the shadow of a tower standing on level ground 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 (√3+1)xmetres.

The length of the shadow of a tower standing on level ground 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 (√3+1)x
metres.