Question

When the sun is at an elevation of ${35}^{\circ }$, the shadow of a tree is 10 m. What would be the length of the shadow, when the sun is at an elevation of ${25}^{\circ }$?

$\left[\begin{array}{c}Tan{25}^{\circ }=0.46\\ Tan{35}^{\circ }=0.7\end{array}\right]$

• A. 21.32 m
• B. 12.42 m
• C. 18.24 m
• D. 15.21 m

Answer 1

The correct option is D

15.21 m

From the figure, we can see that

When the angle of elevation is ${35}^{\circ }$, length of the shadow is CB = 10

Let height AB $\equiv$ H.

In $△$ AFC

$Tan{35}^{\circ }=\frac{FC}{AF}$

$0.7=\frac{H}{10}$ $(AF=CB=10m)$

H = 10 $\times 0.7=7m$

In $△AED$

Tan ${25}^{\circ }=\frac{ED}{AE}$

0.46 = $\frac{H}{AE}=\frac{7}{AE}$

AE =$\frac{7}{0.46}=15.21$ m

Hence, the length of shadow when angle of elevation is ${25}^{\circ }$ is equal to BD = AE = 15.21 m