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The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?

The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder? Correct Answer <span class="math-tex">\(6\sqrt 2 \ m\)</span>

Given:

The angle of elevation of a ladder leaning against a wall = 45°

The length of the ladder is 12 m

Concept used:

cos θ = Base/Hypotenuse

Calculation:

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From the following figure

AC is ladder

AC = 12 m

In ΔABC

⇒ cos 45° = BC/AC

⇒ 1/√2 = BC/12

⇒ BC = 12/√2

⇒ BC = 6√2

∴ The distance between the wall and the foot of the ladder is 6√2 m

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