Question

6.) you are standing 50 meters from a hot air balloon that is preparing to take off. the angle of elevation to the top of the balloon is 28°. find the height of the balloon.

Explanation:

Step1: Set up tangent ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the angle of elevation $\theta = 28^{\circ}$, the adjacent side to the angle of elevation is the distance from the person to the balloon ($x = 50$ meters), and the opposite side is the height of the balloon ($h$). So, $\tan(28^{\circ})=\frac{h}{50}$.

Step2: Solve for height $h$

Multiply both sides of the equation $\tan(28^{\circ})=\frac{h}{50}$ by 50. We get $h = 50\times\tan(28^{\circ})$.
Since $\tan(28^{\circ})\approx0.5317$, then $h=50\times0.5317 = 26.585\approx26.59$ meters.

Answer:

$26.59$ meters