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.

Question

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.

Answer 1

The distance she needs to throw the ball can be found using the Pythagorean Theorem. We can consider the distances from the shortstop to second base and from second base to first base as the legs of a right triangle, and the distance she needs to throw the ball as the hypotenuse.

Using the Pythagorean Theorem, we have:

Distance^2 = (Distance to second base)^2 + (Distance from second base to first base)^2

Distance^2 = 30^2 + 90^2
Distance^2 = 900 + 8100
Distance^2 = 9000

Taking the square root of both sides:

Distance = √9000

Distance ≈ 94.9

Therefore, she needs to throw the ball approximately 94.9 feet.

Answer 2

To solve this problem, we can use the Pythagorean theorem.

The distance from the shortstop to first base is the hypotenuse of a right triangle, with the distance from second base to first base being one of the legs and the distance from the shortstop to second base being the other leg.

Using the Pythagorean theorem, we have:

(distance to first base)^2 = (distance from second base to first base)^2 + (distance from shortstop to second base)^2

Let's solve for the distance to first base:

(distance to first base)^2 = (0 ft)^2 + (30 ft)^2

(distance to first base)^2 = 0 + 900

(distance to first base)^2 = 900

Now, take the square root of both sides to find the distance to first base:

distance to first base = sqrt(900)

distance to first base = 30 ft

So, the shortstop needs to throw the ball approximately 30 feet to reach first base.

Answer 3

To find the distance the shortstop needs to throw the ball, we can use the Pythagorean theorem. The base path between second and third base forms one side of a right triangle, with the distance from the shortstop to second base being the other side, and the distance from the shortstop to first base being the hypotenuse.

Let's call the distance from the shortstop to second base "a" and the distance from the shortstop to first base "c". We want to find the value of "c".

According to the problem, the distance from the shortstop to second base (a) is given as 30 feet.

Using the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), we can set up the equation:

c^2 = a^2 + b^2

Since the base path between second and third base is a right angle, we can assume that the distance from second base to first base is the same as the distance from third base to first base. So, the value of "b" is also 30 feet.

Plugging in the values, we get:

c^2 = 30^2 + 30^2

c^2 = 900 + 900

c^2 = 1800

To solve for "c", we take the square root of both sides:

c = √(1800)

Using a calculator, we find that c ≈ 42.4 feet.

Therefore, the shortstop needs to throw the ball approximately 42.4 feet to reach first base.