Question

A ladder reaches a point on a wall which is 20 m above the ground and its foot is $20\sqrt{3}$ m away from the ground. The angle made by the ladder with the wall is

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Let the angle made by the ladder be $\theta$

$tan\theta =\frac{BC}{AB}$

$=\frac{20\sqrt{3}}{20}$

$=\sqrt{3}$

$\tan \theta =\sqrt{3}$

∴$\theta ={60}^0$ [since $\tan {60}^0=\sqrt{3}$]