# DBT JRF 2022 — Question 18

Exam: DBT JRF 2022 · Section: A · Topic: Aptitude › Trigonometry & Geometry · Difficulty: Medium

## Question

A ladder leaning against a wall is making an angle of 60° with the ground. If the length of the ladder is 18 m, find the distance of the foot of the ladder from the wall.

## Options

- **A.** $9\sqrt{3}$ m
- **B.** 9 m
- **C.** $18/\sqrt{2}$ m
- **D.** $18/\sqrt{3}$ m

## Answer

Option B

## Explanation

Ladder-wall trigonometry problem: Given: Ladder length = 18 m, angle with ground = 60°. The distance from the foot of the ladder to the wall is the adjacent side of the right triangle: $d = L \cos\theta = 18 \times \cos 60° = 18 \times 0.5 = 9\,\text{m}$ The height reached on the wall (opposite side): $h = L \sin\theta = 18 \times \sin 60° = 18 \times \frac{\sqrt{3}}{2} = 9\sqrt{3}\,\text{m}$ Note: Option 1 ( $9\sqrt{3}$ m) is the HEIGHT on the wall, not the distance from the wall. The correct answer for the distance from the wall is 9 m (Option 2). Distractor Option 4 ( $18/\sqrt{3} = 6\sqrt{3} \approx 10.4\,\text{m}$ ) is incorrect.

Source: https://mypyqbuddy.com/questions/a-ladder-leaning-against-a-wall-is-making-6a104cd5920734408bc0c6ef