# A ladder makes an angle of 60^@ to a pole. What angle would be made by a ladder, which is three times longer than this ladder, on a pole of same height?

Apr 5, 2017

Longer ladder makes an angle of ${16.78}^{\circ}$

#### Explanation:

Let the longer ladder whose length is say $x$ make an angle of $\theta$. The picture appears as one given below.

Therefore $\frac{h}{x} = \sin {60}^{\circ} = \frac{\sqrt{3}}{2}$

or $x = \frac{2 h}{\sqrt{3}}$

Hence length of longer ladder is $3 \times \frac{2 h}{\sqrt{3}} = 2 \sqrt{3} h$

and $\sin \theta = \frac{h}{2 \sqrt{3} h} = \frac{1}{2 \sqrt{3}} = \frac{\sqrt{3}}{6} = 0.2887$

and $\theta = {\sin}^{- 1} 0.2887 = {16.78}^{\circ}$

Hence, longer ladder makes an angle of ${16.78}^{\circ}$