Question

you are in a hot air balloon that is 600 feet above the ground. if the angle from your line of sight to your friend is 20°, how far is he from the point on the ground.

Answer 1

x = 164.9 ft

Step-by-step explanation:

Given the following figures

To find the distance from the point on the ground, we need to apply the SOH CAH TOA

`\begin{gathered} \text{Height = 600 ft} \\ \text{Horizontal distance x} \\ \theta\text{ = 20} \\ \text{ }\tan \theta\text{ =}\frac{opposite}{\text{adjacent}} \\ \text{opposite = 600 ft} \\ \text{adjacent = x ft} \\ \tan \text{ 20 = }(600)/(x) \\ \text{Cross multiply} \\ x\cdot\text{ tan 20 = 600} \\ \text{x = }\frac{600}{\tan \text{ 20}} \\ \tan \text{ 20 = }0.3639 \\ \text{x = }(60)/(0.3639) \\ \text{x = }164\text{ .9 ft} \end{gathered}`

Therefore, the distance is 164.9 ft