If from the top of a tower, 60 metres high, the angles of depression of the top and floor of a house are 30 o and 60 o respectively, then the height (in metres) of the house is

Step-by-step solution

Let d be the distance between the tower and house ∴ d = 60 cot ⁡ 60 o ⇒ d = 60 - h cot ⁡ 30 o ⇒ 60 cot ⁡ 60 o = 60 - h cot ⁡ 30 o ⇒ h = 60 3 - 1 3 3 = 40 m