Question

Sam is looking at the roof of the adjacent building from top of his flat. His height is $5$ feet. The height of his building as well as the distance between the two buildings is $50$ feet. Sam measures the angle of elevation of his line of sight to the top of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building?

• A. 55feet
• B. 10√3feet
• C. 55+10√3 feet
• D. 60cm

Answer 1

The correct option is C

55+10√3 feet

The height of the adjacent building is $=AB+BC+CD$

We know that $BC=\text{height of Sam}=5$ feet

$CD=\text{height of Sam’s building}=50$ feet

Consider the right triangle $△ABO,$

It is given that, $OB=\text{Distance between the buildings}=50$ feet

Therefore, $\frac{AB}{OB}=\tan {30}^{\circ }$

$\Rightarrow AB=OB\times \tan {30}^{\circ }$

$\Rightarrow AB=\frac{50}{\sqrt{3}}$ feet

Therefore, the height of the adjacent building $=\frac{50}{\sqrt{3}}+50+5=55+\frac{50}{\sqrt{3}}$ feet