Question

a tower that is 127 feet tall casts a shadow 157 feet long. find the angle of elevation of the sun to the nearest degree. the angle of elevation is degrees. (round to the nearest degree.)

Explanation:

Step1: Identify right - triangle relationship

We have a right - triangle where the height of the tower is the opposite side ($a = 127$) and the length of the shadow is the adjacent side ($b = 157$) with respect to the angle of elevation $\theta$. The tangent function is $\tan\theta=\frac{a}{b}$.

Step2: Calculate the tangent value

$\tan\theta=\frac{127}{157}\approx0.8089$.

Step3: Find the angle

$\theta=\arctan(0.8089)$. Using a calculator, $\theta\approx39.3^{\circ}$.

Step4: Round to the nearest degree

Rounding $39.3^{\circ}$ to the nearest degree gives $39^{\circ}$.

Answer:

$39$