Question

The angle of elevation of the top of a tower from two places situated at distances $21m\text{and}xm$ from the base of the tower are $45°\text{and}60°$ respectively. What is the value of $x$?

• A. $7\sqrt{3}$
• B. $7-\sqrt{3}$
• C. $7+\sqrt{3}$
• D. $14$

Answer 1

The correct option is A

$7\sqrt{3}$

Explanation for correct option:

Step 1: Finding the height of the tower(h):

Let B and C be those two points situated at the given distance and A be the top of the tower.

Let's consider $△ABD$,

$\begin{array}{rcl}\tan {45}^{°}& =& \frac{AD}{BD}\\ 1& =& \frac{h}{21}\left[\because \tan {45}^{°}=1\right]\\ h& =& 21m\end{array}$

Step 2: Finding the value of $x$:

Let's consider $∆ADC$,

$\begin{array}{rcl}\tan {60}^{°}& =& \frac{AD}{DC}\\ \sqrt{3}& =& \frac{h}{x}\left[\because \tan {60}^{°}=\sqrt{3}\right]\\ \sqrt{3}& =& \frac{21}{x}[\because h=21]\\ x& =& \frac{21}{\sqrt{3}}\\ & =& \frac{7\times 3}{\sqrt{3}}\\ & =& \frac{7\times \sqrt{3}\times \sqrt{3}}{\sqrt{3}}\\ x& =& 7\sqrt{3}m\end{array}$

Hence, option (A) is the correct answer.