Question

A window of a house is h m high above the ground. The angle of elevation and depression of the top and the foot of another house on the opposite side of the street are a and respectively. Prove that height of another house is h(1 + tan α cot β)

Answer 1

Let AB is a house and A be the window of the house,. then AB = h m

Let CD is a another house of height H meter then

∠ADB = ∠PAD = β (Alternate Angle)

From right angled ∆APC,

Put the value in equation (iii) from equation (i),

h cot β = (H – h) cot α

h cot β = H cot α – h cot α

⇒ h cot β + h cot α = H cot α

Hence, height of another house is h(1 + tan α cot β)m.