Question

trig mixed practice
6 of 9
desmos | graphing calculator | texas version
you are in a hot air balloon. you look at steve with an angle of depression of 30 degrees. your elevation is 1200 feet. how far apart are you and steve?
○ 2400 feet
○ 600 feet
○ 692 feet
○ 1039 feet

Explanation:

Step1: Define right triangle components

Let $h = 1200$ ft (vertical elevation, opposite side to the angle of depression), $\theta = 30^\circ$ (angle of depression, equal to the angle of elevation from Steve to the balloon), and $d$ = straight-line distance between balloon and Steve (hypotenuse).

Step2: Apply sine trigonometric ratio

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{d}$
Rearrange to solve for $d$:
$d = \frac{h}{\sin(\theta)}$

Step3: Substitute values and calculate

Substitute $h=1200$ ft, $\sin(30^\circ)=0.5$:
$d = \frac{1200}{0.5} = 2400$

Answer:

2400 feet