Question

A hawk is flying above the ground at an elevation of 50 feet above the ground. It's prey is approximately at a 15 degree angle of depression. How far is it from its prey?

Answer 1

The distance between the hawk and its prey is approximately 13.03 feet.

Step-by-step explanation:

To find the distance between the hawk and its prey, we can use trigonometry. The angle of depression refers to the angle formed by a horizontal line and the line connecting the hawk and its prey. In this case, the angle of depression is 15 degrees.

Let's assume that the distance between the hawk and its prey is x feet. The opposite side of the angle of depression is x feet, and the adjacent side is the elevation above the ground, which is 50 feet. We can use the tangent function to calculate the distance:

tan(15°) = x/50

Now, we can solve for x:

x = 50 * tan(15°)

Using a calculator, we find that x is approximately 13.03 feet. Therefore, the hawk is approximately 13.03 feet away from its prey.