Question

question 5 of 5
select the correct answer.
a helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram. how far is the object from the helicopter to the nearest foot?
268 feet
651 feet
90 feet
698 feet

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the side opposite the $21^\circ$ angle equal to 250 ft, and we need the hypotenuse (distance from helicopter to object). Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Rearrange for hypotenuse

Let $x$ = hypotenuse. Rearrange the formula:
$x = \frac{\text{opposite}}{\sin(\theta)}$

Step3: Substitute values

Substitute $\theta=21^\circ$, opposite=250 ft:
$x = \frac{250}{\sin(21^\circ)}$
Calculate $\sin(21^\circ) \approx 0.3584$, so:
$x \approx \frac{250}{0.3584} \approx 697.5$

Step4: Round to nearest foot

$x \approx 698$

Answer:

698 feet