Problem 5) A player is standing on a basketball court. The angle of elevation from the foot of the player to a 10 foot high basket is 30 degrees. How far is the player from the base of the basketball pole?
We can use trigonometry to solve this problem.
Let x be the distance from the player to the base of the basketball pole.
Since the angle of elevation is 30 degrees, we can draw a right triangle where the opposite side is 10 feet (the height of the basket), the hypotenuse is the distance from the player to the basket, and the adjacent side is x.
Using the sine function, we have:
sin(30) = opposite/hypotenuse
sin(30) = 10/x
We can solve for x by multiplying both sides of the equation by x:
x * sin(30) = 10
Dividing both sides by sin(30):
x = 10 / sin(30)
Using a calculator, we find:
x ≈ 20.0 feet
Therefore, the player is approximately 20.0 feet from the base of the basketball pole.