Question

a building 57.31 feet tall has a shadow that is 62.69 feet long. find the angle of elevation of the sun to the nearest hundredth of a degree.
the angle of elevation is
(round to the nearest hundredth as needed.)

Explanation:

Step1: Set up tangent ratio

We know that in a right - triangle formed by the building, its shadow, and the line of sight to the sun, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, where $\theta$ is the angle of elevation, the height of the building is the opposite side, and the length of the shadow is the adjacent side. So, $\tan\theta=\frac{57.31}{62.69}$.

Step2: Calculate the angle

We have $\theta = \arctan(\frac{57.31}{62.69})$. Using a calculator, $\frac{57.31}{62.69}\approx0.9142$. Then $\theta=\arctan(0.9142)$. $\theta\approx42.45^{\circ}$.

Answer:

$42.45$