### Theory:

Let us learn how to solve real-life situations based on the angle of depression.
Example:
1. A man observes the ball, which is at a distance of $$1.5 \ m$$ from him. If the angle of depression is $$45^{\circ}$$, then find the height of the man.

Solution:

Let $$AB$$ denote the height of the man and $$BC$$ denote the distance of the man from the ball.

From the given data, we have:

$$\theta = 45^{\circ}$$, and $$BC = 1.5 \ m$$

To find: The height of the man ($$AB$$).

Explanation:

In the right $$\triangle ABC$$, $$tan \ \theta = \frac{BC}{AB}$$

$$tan \ 45^{\circ} = \frac{1.5}{AB}$$

$$1 = \frac{1.5}{AB}$$

$$AB = 1.5 \ m$$

Therefore, the height of the man is $$1.5 \ m$$.

2. A man observes a ball which is at a distance of $$1.2 \sqrt{3} \ m$$ from him. If the height of the man is $$1.2 \ m$$, then find the angle of depression.

Solution:

Let $$AB$$ denote the height of the man and $$BC$$ denote the distance of the man from the ball.

From the given data, we have:

$$AB = 1.2 \ m$$, and $$BC = 1.2 \sqrt{3} \ m$$

In the right angled triangle $$ABC$$, $$tan \ \theta = \frac{BC}{AB}$$

$$tan \ \theta = \frac{1.2 \sqrt{3}}{1.2}$$

$$tan \ \theta = \sqrt{3}$$

$$\theta = 60^{\circ}$$

Therefore, the angle of depression is $$60^{\circ}$$.
Important!
The angle of elevation and angle of depression are equal because they are alternate angles.