Find the length of the base of the following pyramid, given the height of the pyramid is 71 meters and the angle of elevation of the base of the pyramid is 42°. Round to the nearest whole number.
Let's denote the length of the base of the pyramid as $x$.
From the given information, we know that the height of the pyramid is 71 meters. This forms a right angle triangle with the base of the pyramid. The angle of elevation of the base of the pyramid, which is the angle between the base and the line of sight of the observer, is 42°.
By definition of angle of elevation, we know that the tangent of the angle of elevation is equal to the ratio of the height to the distance from the observer to the base of the pyramid.
Therefore, we have $\tan(42°) = \frac{71}{x}$.
To find $x$, we can rearrange the equation:
$x = \frac{71}{\tan(42°)} \approx \frac{71}{0.9004} \approx 78.844$.
Rounding to the nearest whole number, the length of the base of the pyramid is $\boxed{79}$ meters.