Question

A $15m$ 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?

• A. $7.34m$
• B. $8m$
• C. $9.46m$
• D. $6.96m$

Answer 1

The correct option is D $6.96m$

Let ${}^{\prime }{h}^{\prime }$ is the distance of broken point from the top of ladder

Now, in $△ABC$

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

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

$\Rightarrow \sqrt{3}h=30-2h$

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

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

$\Rightarrow h=30(2+\sqrt{3})=60-30\sqrt{3}=60-51.96=8.04m$

$\therefore$ Height of ladder from the ground $=15-h$

$=15-8.04$

$=6.96m.$

Hence, the answer is $6.96m.$