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:
 
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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:
 
2.png
 
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.
 
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