Question

A man on the roof of a house, which is 10 m high, observes the angle of elevation of the building as 42° and angle of depression of the base of the building as 40°. Find the height of the building and its distance from the house.

Answer 1

Let AB be the house and CD be the building. Let the height of the building be h m and let x m be the distance between the house and the building. Let AE be ⊥ CD. Then, CD = h m, CE = (h – 10) m 

In ∆ABD, \(\frac{BD}{AB}\) = tan 50° ⇒ \(\frac{x}{10}\) = 1.1918 ⇒ \(x\) = 11.918

In ∆CAE, \(\frac{CE}{AE}\) = tan 42° ⇒ \(\frac{h-10}{x}\) = 0.9004           [Using t – tables] 

⇒ h – 10 = 0.9004 \(x\) = 0.9004 × 11.9.18 = 10.731 

⇒ h = 10.731 + 10 = 20.73 

Hence, height of the building = 20.73 m and distance between house and the building = 11.92 m (approx).