Question

How far is the house from the pilot of the ballon?

Answer 1

4936 ft

Explanation:

We have the following:

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

To better understand the question, we make a sketch of the situation:

Therefore, determine the distance using the trigonometric sine function, as follows:

`\begin{gathered} \sin\theta=\frac{\text{ opposite }}{\text{ hypotenuse}} \\ \\ \theta=34\degree \\ \\ \text{opposite = 2760} \\ \\ \text{hypotenuse = x} \\ \\ \text{ we replacing:} \\ \\ \sin34\degree=(2760)/(x) \\ \\ x=(2760)/(\sin34\degree) \\ \\ x=4935.7\cong4936\text{ ft} \end{gathered}`

Therefore, the house is 4936 feet from the pilot of the ballon