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)?
What is 50*cotangent20 ? I get about 140 feet.
oops, you want the hypotenuse (I gave you the horizontal distance)
Hypotenuse= 50/sin20
To find the distance from John's seat to the court (length of the hypotenuse), we can use trigonometry and the concept of right triangles.
Let's denote the distance from John's seat to the court as "x" (length of the hypotenuse), and the height difference between John's seat and the court as "y" (opposite side of the triangle). The angle of depression, 20 degrees, is the angle between the horizontal line (adjacent side) and the line of sight from John to the court.
In this case, we have a right triangle where the opposite side is known (y = 50 ft) and the angle of depression (20 degrees) is given. We can use the trigonometric function "tangent" to solve for x.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, we have:
tan(20 degrees) = y / x
Rearranging the equation to solve for x, we have:
x = y / tan(20 degrees)
Substituting the known values:
x = 50 ft / tan(20 degrees)
To get the answer, we can use a scientific calculator or trigonometric tables to find the tangent of 20 degrees, and then divide the height difference, 50 ft, by this tangent:
x ≈ 50 ft / 0.364
x ≈ 137.36 ft
Therefore, the court is approximately 137.36 feet away from John's seat.