Question

2 multiple choice 1 point a park ranger is looking out from their station at a 30 degree angle of depression. the ranger is 80 feet above the ground. how far is it from the ranger up in the station down to the fire? round to the nearest hundredth. 92.38 feet 138.56 40 feet 160 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height (opposite side to the angle of depression) is 80 feet and we want to find the hypotenuse $x$. The angle of depression is 30 degrees, and the angle in the right - triangle is also 30 degrees. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(30^{\circ})=\frac{80}{x}$

Step2: Solve for $x$

Since $\sin(30^{\circ})=\frac{1}{2}$, we can rewrite the equation as $\frac{1}{2}=\frac{80}{x}$. Cross - multiply to get $x = 160$ feet.

Answer:

D. 160 feet