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A 16 m high tree fall on a wall in such a way that it touches the mid-point of the height of a wall. If the angle of elevation from the base of the tree to the point where the tree touches the wall is 30°, then find the height of the wall.

A 16 m high tree fall on a wall in such a way that it touches the mid-point of the height of a wall. If the angle of elevation from the base of the tree to the point where the tree touches the wall is 30°, then find the height of the wall. Correct Answer None of these

Let the height of the wall be 2x.

The height of the tree = 16 m

Angle of elevation = 30°

The given conditions can be shown as:

[ alt="trigonometric question1" src="//storage.googleapis.com/tb-img/production/21/02/trigonometric%20question1.png" style="width: 450px; height: 435px;">

Then,

⇒ sin ∠D = BC/BD

⇒ sin 30° = x/16

⇒ 1/2 = x/16

⇒ x = 8 m

∴ The height of the wall is 2x = 16 m.

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