Question

sports the distance between each base on a baseball infield is 90 feet. the third baseman throws a ball from third base to point p. to the nearest foot, how far did the player throw the ball? ft 2nd base 90 ft infield 30 ft 3rd base 1st base home plate

Explanation:

Step1: Use Pythagorean theorem for right - triangle.

The right - triangle has sides \(a = 90\) ft and \(b=90 + 30=120\) ft. The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse (the distance from third base to point \(P\)).

Step2: Calculate \(a^{2}\) and \(b^{2}\).

\(a = 90\), so \(a^{2}=90^{2}=8100\); \(b = 120\), so \(b^{2}=120^{2}=14400\).

Step3: Calculate \(a^{2}+b^{2}\).

\(a^{2}+b^{2}=8100 + 14400=22500\).

Step4: Calculate \(c\).

\(c=\sqrt{22500}=150\) ft.

Answer:

150