If from the top of a tower, 60 metres high, the angles of...

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 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

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

Correct answer

Step-by-step solution

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

Let $d$ be the distance between the tower and house
$∴ d = 60cot {60}^{o}$
$⇒ d = \left(60 - h\right)cot {30}^{o}$
$⇒ 60cot {60}^{o} = \left(60 - h\right)cot {30}^{o}$
$⇒ h = \dfrac{60\left(\sqrt{3} - \dfrac{1}{\sqrt{3}}\right)}{\sqrt{3}} = 40m$

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