Answer
The increase in altitude of the driver round to the nearest foot is \[436\text{ feet}\].
Work Step by Step
Angle of elevation in reference to an object as visualized by observer can be referred as the angle between the horizontal and the line from the object to the eye of the observer.
Increase in altitude means the length of \[BC\], which has been showcased as \[a\]. The side adjacent to angle of elevation of \[5{}^\circ \]has been showcased as \[b\]. Compute the length of \[a\]using the trigonometric function of Sine as follows:
\[\begin{align}
& \text{Sin}\theta =\tfrac{\text{Side opposite to angle}}{\text{Hypotenuse}} \\
& \text{Sin}5{}^\circ =\tfrac{a}{AB} \\
& \text{Sin}5{}^\circ =\tfrac{a}{5,000} \\
& 0.0871557=\tfrac{a}{5,000}
\end{align}\]
On cross multiplying both sides by \[5000\], we get
\[\begin{align}
& a=0.0871557\times 5,000 \\
& a=435.778
\end{align}\]
Hence, the increase in altitude of the driver round to the nearest foot is \[436\text{ feet}\].
