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

Question

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,

MARKS App · Accepted Answer

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

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