Question

A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:

• A. $14\sqrt{3}$ m
• B. 7 m
• C. 14 m
• D. $7\sqrt{3}$ m

Answer 1

The Correct Option is B

The height of the wall is the side adjacent to the angle. Using the formula:
\[\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}\]
Substitute:
\[\cos 60^\circ = \frac{\text{Height}}{14}\]
\[\frac{1}{2} = \frac{\text{Height}}{14} \implies \text{Height} = 7 \, \text{m}\]