Question

A ladder 15 m long makes an angle of \( 60^\circ \) with the wall. Find the height of the point on the wall where the ladder touches the wall.

Hint:

For problems involving ladders leaning against walls, use trigonometric functions like sine and cosine.

Answer 1

Using trigonometry, the height of the point where the ladder touches the wall is given by:
\[ h = L \sin \theta. \] \[ h = 15 \sin 60^\circ. \] \[ = 15 \times \frac{\sqrt{3}}{2}. \] \[ = \frac{15\sqrt{3}}{2}. \] Approximating \( \sqrt{3} = 1.732 \):
\[ h = \frac{15 \times 1.732}{2} = \frac{25.98}{2} = 12.99 \approx 13 \text{ m}. \]