Solve the problem.
-From a balloon 1197 feet high, the angle of depression to the ranger headquarters is 50°21'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?
A) 982 ft
B) 987 ft
C) 997 ft
D) 992 ft

Question

Quizplus · Accepted Answer

To find the distance from the point directly below the balloon to the ranger headquarters, we can use the tangent of the angle of depression, which is equal to the opposite side (the height of the balloon) over the adjacent side (the distance we're trying to find). The tangent of 50°21' can be calculated or looked up, and the formula to use is:$$ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} $$Given:- $\theta = 50°21'$- Opposite (height of the balloon) = 1197 ftRearranging the formula to solve for the adjacent side (distance to headquarters), we get:$$ \text{Adjacent} = \frac{\text{opposite}}{\tan(\theta)} $$Plugging in the values:$$ \text{Adjacent} = \frac{1197}{\tan(50°21')} $$Using a calculator to find $\tan(50°21')$ and solving gives a distance of approximately 992 feet to the nearest foot.

Solve the Problem. -From a Balloon 1197 Feet High, the Angle of Depression