Question

1. the angle of depression from the top of a cliff 800 meters high to the base of a log cabin is 37°20. how far is the cabin from the foot of the cliff? tan 37°20 = 800/x.7627 = 800/x.7627x = 800 1049

Explanation:

Step1: Convert angle to decimal degrees

First, convert $37^{\circ}20'$ to decimal - degrees. Since $1^{\circ}=60'$, then $20'=\frac{20}{60}\approx0.333^{\circ}$, so $37^{\circ}20'\approx37.333^{\circ}$.

Step2: Set up tangent equation

Let the distance between the cabin and the foot of the cliff be $x$. We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 37.333^{\circ}$ and the height of the cliff (opposite side) is $800$ meters. So, $\tan(37.333^{\circ})=\frac{800}{x}$.

Step3: Solve for $x$

We know that $\tan(37.333^{\circ})\approx0.7627$. Then, $0.7627=\frac{800}{x}$, and $x=\frac{800}{0.7627}\approx1049$ meters.

Answer:

The cabin is approximately $1049$ meters from the foot of the cliff.