Question

the figure shows a flagpole and its shadow. the shadow has a length of 43 feet and the suns rays make an angle of 30° with the ground. what is the approximate height, x, of the flagpole? a. 25 feet b. 22 feet c. 28 feet d. 37 feet

Explanation:

Step1: Use tangent function

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 30^{\circ}$, the adjacent side to the angle is the length of the shadow ($43$ feet), and the opposite side is the height of the flagpole $x$. So, $\tan30^{\circ}=\frac{x}{43}$.
Since $\tan30^{\circ}=\frac{\sqrt{3}}{3}$, we have the equation $\frac{\sqrt{3}}{3}=\frac{x}{43}$.

Step2: Solve for $x$

Cross - multiply the equation $\frac{\sqrt{3}}{3}=\frac{x}{43}$ to get $3x = 43\sqrt{3}$. Then $x=\frac{43\sqrt{3}}{3}$.
We know that $\sqrt{3}\approx1.732$, so $x=\frac{43\times1.732}{3}=\frac{74.476}{3}\approx24.825\approx25$ feet.

Answer:

A. 25 feet