Question

A ladder of length 30 m is leaning against a wall making an angle of 30° with the horizontal. Find the distance between the foot of the ladder and the wall.

• A. 14\(\sqrt3\) m
• B. 15\(\sqrt3\) m
• C. 16\(\sqrt3\) m
• D. 17\(\sqrt3\) m

Answer 1

The Correct Option is B

Given	Value
Ladder Length (\(L\))	30 m
Angle with Horizontal (\(\theta\))	30°

The problem involves finding the distance from the foot of the ladder to the wall, referred to as the horizontal distance (\(x\)). This forms a right triangle with the wall, ladder, and ground.

Using trigonometry, the cosine of an angle in a right triangle is defined as:

\( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)

Here, the adjacent side is the distance \(x\), and the hypotenuse is the ladder length.

\( \cos(30°) = \frac{x}{30} \)

We know \( \cos(30°) = \frac{\sqrt{3}}{2} \), so:

\( \frac{\sqrt{3}}{2} = \frac{x}{30} \)

Solving for \(x\), we multiply both sides by 30:

\( x = 30 \times \frac{\sqrt{3}}{2} \)

This simplifies to:

\( x = 15\sqrt{3} \)

Therefore, the correct distance between the foot of the ladder and the wall is 15\(\sqrt{3}\) m.