Question

When Sun's altitude is ${30}^o$, the shadow of a tower is $15$ meter. What is the length of shadow when Sun's altitude is ${60}^o$

• A. $3m$
• B. $4m$
• C. $5m$
• D. $6m$

Answer 1

The correct option is C $5m$

$\tan \theta =\frac{Altitude}{Base}$

$\tan {30}^{\circ }=\frac{Altitude}{Base}$

$⟹\frac{1}{\sqrt{3}}=\frac{Altitude}{15}$

$⟹Altitude=\frac{15}{\sqrt{3}}=5\sqrt{3}$

Now,

$\tan {60}^{\circ }=\frac{Altitude}{Base}$

$⟹\sqrt{3}=\frac{5\sqrt{3}}{Base}$

$Base=5m$

The length of shadow when Sun's altitude ${60}^{\circ }=5m$

Option C is correct.