Question

From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 63°, as shown below. If the distance between the radio antenna and the library is 24 miles, how many miles high is the balloon? Show your work or explain how you got your answer

Answer 1

Given:

Required:

To find the height of the balloon.

Explanation:

The triangle is a right angle triangle.

let the height of the balloon is h mies.

Then trigonometric ratio

$tan\theta=\frac{opp.}{adj.}$$\begin{gathered} tan63\degree=\frac{24}{h} \\ h=\frac{24}{tan63\degree} \\ h=\frac{24}{1.9626} \\ h=12.2286 \\ h\approx12.2\text{ miles} \end{gathered}$

Final Answer:

The balloon is 12.2 miles high.