Question

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

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the shadow length (adjacent side to the 30° angle) is 43 feet, and the height of the flagpole (opposite side to the 30° angle) is \( x \). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(30^\circ)=\frac{x}{43} \).

Step2: Recall the value of \( \tan(30^\circ) \)

We know that \( \tan(30^\circ)=\frac{1}{\sqrt{3}}\approx0.577 \).

Step3: Solve for \( x \)

Substitute \( \tan(30^\circ)\approx0.577 \) into the equation: \( x = 43\times\tan(30^\circ) \).
Calculate \( 43\times0.577\approx25 \) (after rounding to a reasonable approximation).

Answer:

C. 25 feet