Question 49

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, then find the height of the first tree.

Solution

As per the given question,

Let, 'EC' be the first tree and 'AB' be the second tree.

Height of first tree is '$$80\ m$$' and let height of second tree be '$$x$$'

Then, $$AB = x$$ and $$ED = (80 - x)$$

In $$\triangle EAD$$,

tan $$45^{\circ} = \frac{ED}{AD}$$

$$1 = \frac{80-x}{60}$$

$$x = 20\ m$$

Hence, option A is the correct answer.

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