Question

what is the angle of elevation of the sun when a 45 - ft mast casts a 31 - ft shadow? the angle of elevation is
(simplify your answer. type an integer. round to the nearest degree.)

Explanation:

Step1: Recall tangent function

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the mast is the opposite side and the length of the shadow is the adjacent side. So, $\tan\theta=\frac{45}{31}$.

Step2: Find the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta = \arctan(\frac{45}{31})$.
Calculating $\arctan(\frac{45}{31})\approx55.4^{\circ}$.

Step3: Round to the nearest degree

Rounding $55.4^{\circ}$ to the nearest degree gives $55^{\circ}$.

Answer:

$55$