Question

If the shadow of a tower is 30 m when the sun's altitude is ${30}^{\circ }$ what is the length of the shadow when the Sun's altitude is ${60}^{\circ }$?

• A. $10\sqrt{3}m$
• B. 20 m
• C. 10 m
• D. 12 m

Answer 1

The correct option is C

10 m

Let AB(h ) be the height of the tower when the angle of elevation of the sun is ${30}^{\circ }$ and BD be the shadow of a tower the angle of elevation of Sun is ${60}^{\circ }$. BC = 30 m , angle ACB =${30}^{\circ }$ , Angle ADB= ${60}^{\circ }$ Let AB = h m & BD = x m

In $△$ABC

tan ${30}^{\circ }=\frac{Perpendicular}{base}=\frac{BC}{AB}$

tan ${30}^{\circ }=\frac{BC}{AB}=\frac{h}{30}$

$\frac{1}{\surd 3}=\frac{h}{30}$

h= $\frac{30}{\surd 3}$………………(1)

In $△$ABD

tan ${60}^{\circ }$= $\frac{Perpendicular}{base}=\frac{AB}{BD}$

tan ${60}^{\circ }$ = $\frac{h}{x}$

√3 = $\frac{30\surd 3}{x}$ ( from eq 1)

√3x= $\frac{30}{\surd 3}$

x= $\frac{30}{\surd 3\times \surd 3}=\frac{30}{3}$= 10

x= 10 m

Hence, the length of the shadow of tower when sun's elevation is ${60}^{\circ }$ is 10 m