Question

Cara is standing on the edge of a 15 foot high diving board. Her friend Sierra is Treading Water 45 feet from the spot in the pool directly below Cara. What is the angle of depression from the edge of the diving board to the surface of the water where Sierra is located?

Answer 1

Using the information given in the exercise, you can draw the following diagram:

Where β is the angle of depression (in degrees) from the edge of the diving board to the surface of the water where Sierra is located.

In order to find the measure of the angle of depression, you need to use the following Inverse trigonometric function:

`\beta=arc\tan ((opposite)/(adjacent))`

In this case, you can identify that:

`\begin{gathered} opposite=15 \\ adjacent=45 \end{gathered}`

Therefore, substituting the values, you get the following result:

`\begin{gathered} \beta=arc\tan ((15)/(45)) \\ \\ \beta=18.43\degree \end{gathered}`

The answer is:

`18.43\degree`