Question

The shadow of a vertical tower on a level ground increases by $10$ when the altitude of the sun changes from ${45}^0$ to ${30}^0$. Find the height of the tower, correct to two decimal places.

• A. $14$ m
• B. $13.69$ m
• C. $3.69$ m
• D. $14.69$ m

Answer 1

The correct option is B $13.69$ m

In $△ABC$

$\tan {45}^o=\frac{x}{y}$

$\Rightarrow x=y⟶\left(1\right)$

In $△ABD$

$\tan {30}^o=\frac{x}{y+10}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{x}{x+10}$ {from equation (1)}

$\Rightarrow x+10=\sqrt{3}x$

$\Rightarrow x=\frac{10}{\sqrt{3}-1}$ $\because \sqrt{3}=1.732$

$\Rightarrow x=13.69m$