Question

Two building are facing each other on a road of width $12$ metre. From the top of the first building. Which is $10$ metre high, the angle of elevation of the top of the second is found to be ${60}^o$. What is the height of the second building?

• A. $31.8$
• B. $30.8$
• C. $32.8$
• D. $39.8$

Answer 1

The correct option is B $30.8$

R.E.F image

Let, AB be small building, CD be tall building

$\therefore ED=BA=10m,$ Let $CE=x$

$\because$ In $△ACF$

$tan{60}^{\circ }=\frac{CE}{BE}\Rightarrow \sqrt{3}=\frac{x}{12}$

$\Rightarrow 12\sqrt{3}=x$

$\Rightarrow 12\times 1.732=x$

$\Rightarrow 20.784=x$

Hence, $CD=EC+ED$

$=20.784+10m$

$=30.784m$

Thus, req high of second building will be of $30.784m.$