The angle of elevation of a ladder leaning against a wall is 45° and the foot of the ladder is 8 m away from the wall. What is the length of the ladder?

The angle of elevation of a ladder leaning against a wall is 45° and the foot of the ladder is 8 m away from the wall. What is the length of the ladder? Correct Answer 11.31 m

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Given,

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

The foot of the ladder away from the wall = 8 m

Formula:

cos θ = Base/Hypotenuse

Calculation:

From the following figure

AC is ladder

BC = 8 m

In ΔABC

⇒ cos 45°=BC/AC

⇒ 1/√2 = 8/AC

⇒ AC = 8 √2

⇒ AC = 8 × 1.414

⇒ AC = 11.31

∴ Length of the ladder is 11.31 m.