Question

possible points: 1
the angle of depression from the top of a flagpole to the base of a school building is $50^{\circ}$. if the flagpole is 42 feet tall, how far is the flagpole from the base of school building? round your answer to the nearest foot.

Explanation:

Step1: Identify right triangle relationships

The angle of depression equals the angle of elevation from the building base to the flagpole top, so we have a right triangle with opposite side (flagpole height) $42$ ft, angle $50^\circ$, and adjacent side $x$ (distance we need to find).

Step2: Use tangent trigonometric ratio

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, so substitute values:
$\tan(50^\circ) = \frac{42}{x}$

Step3: Rearrange to solve for $x$

Rearrange the formula to isolate $x$:
$x = \frac{42}{\tan(50^\circ)}$

Step4: Calculate the value

Use $\tan(50^\circ) \approx 1.191753592$:
$x \approx \frac{42}{1.191753592} \approx 35.24$

Step5: Round to nearest foot

Round $35.24$ to the nearest whole number.

Answer:

35 feet