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 m, angle with ground = 45°.
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:
\[\cos 45^\circ = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{BC}{10}\]
\[BC = 10 \times \cos 45^\circ = 10 \times \frac{1}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 5\sqrt{2} m\]