Answer
The angle of elevation is known as the angle formed between the line parallel to horizon and the line of vision above observer. Angle of depression is an angle formed between the horizontal line and the line of sight below the observer.
Work Step by Step
The longest side of the right triangle is known as hypotenuse. There is an acute angle and a right angle in right angle triangle. The two legs of the triangle are related to an acute angle. One leg is known as side opposite to the acute angle and other leg is side adjacent to the acute angle. Angle of elevation and the angle of depression are formed by the line parallel to horizon and the line of vision above and below the observer, respectively.
Example:
It is required to compute angle of elevation and angle of depression.
The height of the tower is\[40\text{ ft}\]. The length of the side adjacent to the tower is\[60\text{ ft}\]. Since, the angle of elevation is opposite to the height of the tower and next to the base of the tower, use the tangent ratio formula:
\[\tan \theta =\frac{a}{b}\]
where, a is the side opposite to the angle and b is the side adjacent to the angle. Here, a is\[40\text{ ft}\]and b is \[60\text{ ft}\]. Compute \[\tan \theta \]as shown below:
\[\begin{align}
& \tan \theta =\frac{40\text{ ft}}{60\text{ ft}} \\
& \tan \theta =0.67\text{ ft} \\
& \theta ={{\tan }^{-1}}\left( 0.67 \right) \\
& \theta =33.82
\end{align}\]
\[\approx 34{}^\circ \]
The angle of depression, which the tower made can be computed as follows:
\[\begin{align}
& \text{Angle of depression}=90{}^\circ -\tan \theta \\
& =90{}^\circ -34{}^\circ \\
& =56{}^\circ
\end{align}\].
Hence, the angle of elevation is \[{{34}^{o}}\]and the angle of depression is\[56{}^\circ \].
