Trigonometry assignment URGENT!! PLEASE HELP

Question

- The basketball hoop has a height of 3.05m. Measure the distance out from the hoop to the centre circle

If a person holding a basketball at eye level of height 165cm is standing at the centre circle…

1)what is the angle of depression from the hoop to the basketball?

2) What is the shortest throwing distance to get the ball into the hoop?

Answer 1

Part 1

the hoop is 3.05m from the floor; the center of the hoop is 4.3m from the foul shot line as measured along the floor

 

from those two facts, we can calculate the distance from the center of the hoop to the foul shot line, which is 5.3m

 

so, we have a right triangle with sides of 3.05m and 4.3m, and an hypotenuse of 5.3m

 

using the definition of the sine function (opposite/hypotenuse), we get a decimal of 0.578, which is 35^o

 

Part 2

this part is very difficult to calculate because it is dependent on how high the arc of the flight path might be. a player cannot shoot the ball in a straight line, it must have an arc.

 

however, we can imagine that a player can launch the ball with just enough speed so that the ball will cross the rim, and fall into the net. then, the distance will be slightly more than 5.3m

 

we can make a crude estimate based on the fact that the diameter of the hoop is 0.45m; the center of the ball must pass through the center of the hoop (0.225m from the rim); so the approximate distance will be 5.5m