Question

9.) the flagpole in front of cb east casts a shadow 40 feet long when the measurement of the angle of elevation to the sun is 31°. how tall is the flagpole?

Explanation:

Step1: Set up right - triangle relationship

We can consider a right - triangle where the length of the shadow is the adjacent side to the angle of elevation and the height of the flagpole is the opposite side. Let the height of the flagpole be $h$. We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 31^{\circ}$ and the adjacent side length is 40 feet. So, $\tan(31^{\circ})=\frac{h}{40}$.

Step2: Solve for $h$

Multiply both sides of the equation $\tan(31^{\circ})=\frac{h}{40}$ by 40. We get $h = 40\times\tan(31^{\circ})$. Since $\tan(31^{\circ})\approx0.6009$, then $h = 40\times0.6009 = 24.036\approx24$ feet.

Answer:

24 feet