John is an Atlanta Hawks fan with seaon tickets for the past 5 years.John estimates that his seat is about 50 ft higher than the basketball court and he has calculated that he looks onto the court at an angle of depression of 20 degrees. How far away is the court from John's seat (length of hypotenuse)?

To find the distance from John's seat to the basketball court, we need to use trigonometry. We can consider John's seat, the basketball court, and the line of sight (hypotenuse) between them as a right triangle.

Let's denote the distance from John's seat to the basketball court as "x" (length of the hypotenuse), and the height difference between John's seat and the court as "y" (opposite side). The angle of depression is given as 20 degrees.

Using trigonometric functions, we can relate the angle of depression, the opposite side, and the hypotenuse:

tan(angle) = opposite / hypotenuse

In this case:

tan(20 degrees) = y / x

Now, we can solve the equation for "x" (the distance from John's seat to the basketball court):

x = y / tan(20 degrees)

Since John estimates that his seat is about 50 ft higher than the basketball court, we substitute "y" with 50 ft:

x = 50 ft / tan(20 degrees)

To calculate this using a calculator, you would first find the tangent of 20 degrees (tan(20)), and then divide 50 ft by the result.