Question

Two buildings are 140 m apart. The angle of elevation of the top of a building as seen from the top of the other is 30 degrees. If the 2nd building is 60 m tall, how tall is the 1st building?

• A. $83m$
• B. $80.83m$
• C. $84m$
• D. $140.83m$

Answer 1

Answer: (D)

$140.83m$

Let the height of second building be ${}^{\prime }{h}^{\prime }$ meter.

Now, In $△ABE$

$\Rightarrow \tan {30}^0=\frac{AB}{BE}=\frac{(h-60)}{140}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{(h-60)}{140}$

$\Rightarrow h-60=\frac{140}{\sqrt{3}}=\frac{140\sqrt{3}}{3}$

$\Rightarrow h=\frac{140\sqrt{3}}{3}+60=\frac{140\sqrt{3}+180}{3}$

$\Rightarrow h=\frac{242.2+180}{3}=\frac{422.48}{3}$

$\Rightarrow h=140.83m$

Hence, the answer is $140.83m.$