Question

the length of the shadow when the altitude of the sun is ${60}^o$.

• A. $9m$
• B. $5m$
• C. $4m$
• D. $7m$

Answer 1

The correct option is D $7m$

The sun is at a degree of ${30}^0$
And it is given that the length of the shadow of the pole is 21m.
Hence
$\tan {30}^0=\frac{poleheight}{shadowlenght}$
$\frac{1}{\sqrt{3}}=\frac{h}{21}$
$h=\frac{7\times 3}{\sqrt{3}}$
$h=7\sqrt{3}m$
Now the altitude changes to ${60}^0$, however, height of the pole remains constant.
Hence
$\tan \left({60}^0\right)=\frac{poleheight}{shadowlenght}$
$\sqrt{3}=\frac{7\sqrt{3}}{l}$
$l=7m$