Question

from a hot - air balloon, juan measures a 36 degrees angle of depression to a landmark thats 602 feet away, horizontally. whats the balloons vertical distance down to the ground? round your answer to 1 dp.

1. in circle b with (mangle abc = 78^{circ}) and (ab = 10) units, find the length of (overset{\frown}{ac}). round to the nearest hundredth.

Explanation:

Step 1: Recall arc - length formula

The formula for the length of an arc $\widehat{AC}$ of a circle with radius $r$ and central - angle $\theta$ (in degrees) is $s = r\theta\times\frac{\pi}{180}$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the measure of the central angle.

Step 2: Identify values of $r$ and $\theta$

In circle $B$, $r = AB=10$ units and $\theta=m\angle ABC = 78^{\circ}$.

Step 3: Substitute values into the formula

Substitute $r = 10$ and $\theta = 78$ into the formula $s=r\theta\times\frac{\pi}{180}$. We get $s = 10\times78\times\frac{\pi}{180}$.

Step 4: Simplify the expression

First, simplify $10\times78\times\frac{\pi}{180}=\frac{780\pi}{180}=\frac{13\pi}{3}\approx13.61$.

Answer:

$13.61$