Question

if a 61.0 - foot flagpole casts a shadow of 32.0 feet long, what is the angle of elevation of the sun? round to at least the nearest tenth of a degree.
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Explanation:

Step1: Set up the tangent - ratio

The flagpole forms a right - triangle with its shadow. The height of the flagpole is the opposite side and the length of the shadow is the adjacent side with respect to the angle of elevation of the sun. Let $\theta$ be the angle of elevation of the sun. The tangent of an angle in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side $a = 61.0$ feet and the adjacent side $b = 32.0$ feet. So, $\tan\theta=\frac{61.0}{32.0}$.

Step2: Calculate the angle

We know that $\theta=\arctan(\frac{61.0}{32.0})$. Using a calculator, $\theta=\arctan(1.90625)$.
$\theta\approx62.3^{\circ}$

Answer:

$62.3^{\circ}$