A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base.
Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean theorem.
The distance from second base to first base is the hypotenuse of a right triangle. The legs of the triangle are the distance from the shortstop to second base and the distance from the shortstop to first base.
Using the Pythagorean theorem, we have:
distance^2 = (30 ft)^2 + (90 ft)^2
distance^2 = 900 ft^2 + 8100 ft^2
distance^2 = 9000 ft^2
Taking the square root of both sides, we find:
distance = sqrt(9000) ft
Calculating the square root, we get:
distance ≈ 94.9 ft
Rounded to the nearest tenth, the shortstop needs to throw the ball approximately 94.9 feet.