**Trigonometry in Soccer**

Trigonometry in Sports

By: Brittani LeBlanc, Delaney Ledoux, and Joseph O'Neill

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**Trigonometry in Tennis**

**Trigonometry in Basketball**

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