Question

A ladder leaning against a wall makes an angle of 45° with the ground. If the length of the ladder is 10 m, what is the distance of the foot of the ladder from the wall?

• A. \(10\sqrt{2}\) m
• B. \(5\sqrt{2}\) m
• C. \(3\sqrt{2}\) m
• D. \(10\sqrt{2}\) m

Hint:

Use basic trigonometric ratios in right-angled triangles to find distances related to angles and hypotenuse.

Answer 1

The Correct Option is B

Let the ladder length \(= 10 \text{ m}\), angle with ground \(= 45^\circ\).
We need to find the distance of foot of ladder from the wall, i.e., the base \(BC\) in right triangle \(ABC\).
Using trigonometric relation for the base: \[ \cos 45^\circ = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{BC}{10} \] \[ BC = 10 \times \cos 45^\circ = 10 \times \frac{1}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 5\sqrt{2} \text{ m} \]