Geometry

Question Analysis

This question involves Elevation and Depression Angles. The main focus is on using the given angle of elevation and the length of the shadow to find the height of the tree, which requires trigonometric relations.

Key Concept Explanation:

We use the tangent function in a right triangle. In the situation where the tree is vertical, the shadow is horizontal, and the line of sight from the tip of the shadow to the top of the tree forms the hypotenuse of a right triangle. The tangent of an angle of elevation in a right triangle is defined as the ratio of the opposite side (height of the tree in this case) to the adjacent side (length of the shadow).

Step - by - Step Solution:

Let the height of the tree be  meters.

We know that the length of the shadow ( side)  meters and the angle of elevation

The tangent of an angle  in a right triangle is given by

Here,

Since

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