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A $15 m$ long ladder placed vertically along as wall broke in such a way that its top touches ground making an angle of $60^{\circ}$ with it. At what height from the ground did the ladder break?

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7.34 m

8 m

9.46 m

6.96 m

answer is D.

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Detailed Solution

It is given that a
Let h be the distance of the broken point from the top of the ladder.
Now, in

△ ABC

\sin 60 ° = \frac{AC}{AB} = \frac{15 - h}{h}

⇒

\frac{\sqrt{3}}{2} = \frac{15 - h}{h}

⇒

\sqrt{3} h = 30 - 2 h

⇒

(2 + \sqrt{3}) h = 30

⇒

h = \frac{30}{2 + \sqrt{3}}

⇒

h = \frac{30 (2 + \sqrt{3})}{4 - 3}

⇒

h = 30 (2 + \sqrt{3})

⇒

h = 60 - 30 \sqrt{3}

⇒

h = 60 - 51.96

⇒

h = 8.04 m

⇒

15 - h

= 15 - 8.04

⇒

15 - h = 6.96 m

∴

Height of ladder from the ground is

6.96 m .

Hence, the correct option is 4.

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