Answer
The distance across the lake is \[529\text{ yd}\].
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.
The distance across the lake is the side opposite to the angle of elevation which is showcased as \[a\].
Compute the value of \[a\] using the equation of the trigonometric function as follows:
\[\begin{align}
& \text{Tan}\theta =\tfrac{\text{Side opposite to angle}}{\text{Adjacent side to angle}} \\
& \text{Tan}{{40}^{\circ }}=\tfrac{a}{630} \\
& 0.839=\frac{a}{630}
\end{align}\]
On multiplying both sides by \[630\], we get
\[\begin{align}
& a=0.839\times 630 \\
& =529\text{ yd}
\end{align}\]
Hence, the distance across the lake rounded to the nearest yard is \[529\text{ yd}\].
