Question

Sam is looking at the roof of the adjacent building from top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip 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$\sqrt{3}$ feet
• C. 55 + $\frac{50\sqrt{3}}{3}$ feet
• D. 60cm

Answer 1

The correct option is C

55 + $\frac{50\sqrt{3}}{3}$ feet

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

We know that BC = height of Sam = 5 feet

CD = height of Sam’s building = 50 feet

Consider the right triangle ∆ABO,

∠ABO = 90°

It is given that, OB = Distance between the buildings = 50 feet

Therefore, $\frac{AB}{OB}=tan30°$

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

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

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

= (55 + $\frac{50\sqrt{3}}{3}$) feet