Geometry

Trigonometry

Medium

If a 30 meter ladder is placed against a 15 meter wall such that it just reaches the top of the wall, then the elevation of the ladder with wall is?

30°

45°

60°

90°

✅ Correct Option: 1

Let $\theta$ be the angle of elevation of the ladder from the horizontal ground. The ladder forms the hypotenuse of a right triangle, with length $30$ m, while the height of the wall is $15$ m.

Thus, $\sin\theta=\dfrac{15}{30}=\dfrac{1}{2}$ , giving $\theta=30^\circ$ .

Note: The wording 'with wall' is imprecise. The angle between the ladder and the wall would be $60^\circ$ , but the standard angle of elevation is measured from the horizontal, giving the official answer $30^\circ$ .

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Solution

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