Given:
The objective is to explain Pythagorean Theorem with two examples by applying it to sports.
Explanation:
The Pythagorean Theorem states that. in a right triangle the sum of the squares of a two perpendicular legs will be equal to the square of the largest side of the triangle.
Consider a right triangle ∆ABC right angled at B.
By applying the Pythagorean Theorem to the above right triangle,
[tex]AC^2=AB^2+BC^2\text{ . . . . . .(1)}[/tex]Example 1:
Consider a tennis player standing striking the ball to the service line of opponent field.
Let the height of the tennis player will be h = 3m.
The distance between the tennis player and the opponent service line is x = 18m.
Then, the distance at which the tennis player strikes the ground can be calculated as,
From the above diagram the distance d can be calculated using equation (1) as,
[tex]d^2=h^2+x^2\text{ . . . . . . (2)}[/tex]On plugging the values in equation (2),
[tex]\begin{gathered} d^2=3^2+18^2 \\ d^2=9+324 \\ d=\sqrt[]{333} \\ d\approx18.25m \end{gathered}[/tex]Example 2:
Consider a basket ball player ready to take a free throw standing at a horizontal distance of 20 ft from the ring and holding the ball at with distance of 10ft below the ring.
Then, the hypotenuse distance of the ring can be calculated using equation (1) as,
[tex]\begin{gathered} x^2=10^2+20^2 \\ x^2=100+400 \\ x=\sqrt[]{500} \\ x\approx22.36ft \end{gathered}[/tex]Hence, the explanation for Pythagorean Theorem with two examples are provided.
