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# Trigonometry in Sports

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## brittani leblanc

on 13 April 2015

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#### Transcript of Trigonometry in Sports

Trigonometry in Soccer
Trigonometry in Sports
By: Brittani LeBlanc, Delaney Ledoux, and Joseph O'Neill
Picture's Work Cited
Trigonometry in Tennis
In the sport of soccer, trigonometry can be used to master a penalty kick.
One versus one on the goalkeeper, the player taking the penalty kick has a complete advantage with scoring a goal.

The size of a regular soccer net is 8 yards across and 8 feet high
A penalty shot is kicked 11 feet away from the net
the rules say that the goalkeeper must stay on the goal line before the ball is kicked, making it difficult to cut off the angle of the shooter
Based on triangles, there is a certain angle measurement that you can kick the ball at to get perfectly placed into the top right corner

The penalty area is 11 feet away from the net, the net is 8 feet high, and if the keeper is in the center of the net he or she is 12 feet away from the right post when looking at the net
X is the length from the penalty kick area to the post, and y is the length from the penalty kick area to the upper right corner of the net, theta is the unknown angle measurement in which the player needs to kick it to get it perfectly in the upper right hand corner
theta turns out to be 25.558 degrees
Dunking
Leave the ground completely and put the ball in the net over the rim
Dunks are worth 2 points, similar to a layup or jumpshot from inside the 3 point line
Dunks take a lot of skill as one must have really strong legs to jump that high
Let's say you started your jump from 15 feet away from the basket on the baseline
The basket is 10 feet tall
By using Pythagorean Theorem you can find the hypotenuse and have an SSS triangle
The hypotenuse of the triangle would be 18.027 feet long
Then you can find the angle at which you must leave the floor at a straight line to the basket by using the trig ratios represented by SOH CAH TOA
Theta would be approximately 33.69 degrees
Tennis Serve
In a tennis match, a serve is used at the beginning of every rally to start it
The faster and harder the player hits the ball closer to the top of the net, the better the serve is
When serving, you must get the serve in the service box whose limits stretch 60 feet from the baseline where you are serving
Fun Fact: Rafael Nadal, a famous tennis player, has a typical serve speed at around 125 mph

The human body and the ground would create a right angle
The hypotenuse of the triangle would be the track that the ball follows, if hit with enough force, it should follow a straight line down to the other side of the court
This method doesn’t take into account weather conditions affecting the ball or spin on the ball

My Example
Your child is 4.5 feet tall with a racquet peak at about 6 feet tall.
One leg of the triangle would be 60 feet (the furthest point possible but still considered in play in the service box)
The other leg would be the 6 foot tall human from toe to racquet peak
The Hypotenuse would be 60.299 feet and i got that by using the Pythagorean Theorem
Since the 3 side lengths of the triangle are known, you can now use the trigonometric ratios represented by “SOH CAH TOA” to solve for the top angle
You should reach an answer of 84.292⁰ and when solving for bottom angle you should reach an answer of 5.711⁰ after using CAH
This tells you that a 6 foot tall human being from toe to racquet peak would have to hit the ball at an angle of 84.292⁰ to get the ball in play at the farthest possible point in the service box
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