Question

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at ${60}^{\circ }$ Find he angle between the sun rays and the ground at the time of longer shadow.

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${15}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

Let the length of flag staff = $h$

Let the length of shadow at ${60}^{\circ }$ = $s$

Let the angle when the shadow is $3s$ = $\theta$

Then, $\tan \angle$ of elevation = $\frac{Length}{Shadow}$

Now, $\tan 60=\frac{h}{s}$

$h=\sqrt{3}s$

Now, $\tan \theta =\frac{h}{3s}$

$\tan \theta =\frac{s\sqrt{3}}{3s}$

$\tan \theta =\frac{1}{\sqrt{3}}$

$\tan \theta =\tan 30$

$\theta ={30}^{\circ }$