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Question

Mathematics Question on Heights and Distances

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

A

14314\sqrt{3} m

B

7 m

C

14 m

D

737\sqrt{3} m

Answer

7 m

Explanation

Solution

The height of the wall is the side adjacent to the angle. Using the formula:
cos⁡θ=AdjacentHypotenuse\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}
Substitute:
cos⁡60∘=Height14\cos 60^\circ = \frac{\text{Height}}{14}
12=Height14  ⟹  Height=7 m\frac{1}{2} = \frac{\text{Height}}{14} \implies \text{Height} = 7 \, \text{m}