Question

If the length of the shadow of a vertical pole on the horizontal ground is equal to its height, find the angle of elevation of the sun-

• A. ${85}^{\circ }$
• B. ${65}^{\circ }$
• C. ${45}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

In right angle $\Delta PQR$ , $PQ$ represents the vertical pole and $BC$ represents the shadow on the ground.

And $\theta$ be the represents angle of elevation the sun.

Then, we know that

$\tan \theta =\frac{PQ}{QR}=\frac{h}{x}$

But, given that

Length of shadow = Height of the tower

$\tan \theta =\frac{h}{h}=1$

$\tan \theta =\tan {45}^0$

$\theta ={45}^0$

Hence, the angle of elevation of the sun $={45}^0$