Question

a certain flagpole that is 274 feet tall casts a shadow 133 feet long. find the angle of elevation of the sun. the suns angle of elevation is °. (round to the nearest degree as needed.)

Explanation:

Step1: Set up the tangent - ratio

We know that in a right - triangle formed by the flagpole, its shadow, and the line of sight to the sun, the tangent of the angle of elevation $\theta$ is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the flagpole is the opposite side ($a = 274$ feet) and the length of the shadow is the adjacent side ($b = 133$ feet). So, $\tan\theta=\frac{274}{133}$.

Step2: Calculate the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta=\arctan(\frac{274}{133})$.
$\theta=\arctan(2.06015)$.
Using a calculator, $\theta\approx64^{\circ}$.

Answer:

$64$