A baseball diamond is a square with sides of 90 ft. long.
a) to the nearest foot, what is the length of a throw from home to third base...
b) what is the length of a throw from the shortstop position (midway between 2nd and 3rd) to 1st base
a) 90 feet ????
b) x^2 = 90^2 + 45^2
solve for x ( got 100.6 ft)
a) To find the length of a throw from home to third base, we can use the Pythagorean theorem. We need to find the length of the hypotenuse of a right triangle formed by the sides of the baseball diamond.
The two sides of the right triangle are the basepath from home to third base and the basepath from home to first base. Since a baseball diamond is a square with sides of 90 ft long, both sides of the triangle will have a length of 90 ft.
Applying the Pythagorean theorem, we can calculate the length of the hypotenuse:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Plugging in the values, we have:
c^2 = 90^2 + 90^2
c^2 = 8100 + 8100
c^2 = 16200
c ≈ √16200 ≈ 127.28 ft
To the nearest foot, the length of a throw from home to third base is approximately 127 ft.
b) To find the length of a throw from the shortstop position (midway between 2nd and 3rd) to 1st base, we can divide the baseball diamond into two right triangles.
The first triangle consists of the basepath from the shortstop position to third base (45 ft) and the basepath from the shortstop position to first base (45 ft).
Applying the Pythagorean theorem, we can calculate the length of the hypotenuse of the first triangle:
c1^2 = 45^2 + 45^2
c1^2 = 4050 + 4050
c1^2 = 8100
c1 ≈ √8100 ≈ 90 ft
The second triangle consists of the hypotenuse we just found (90 ft) and the basepath from third base to first base (90 ft).
Applying the Pythagorean theorem again, we can calculate the length of the hypotenuse of the second triangle:
c2^2 = 90^2 + 90^2
c2^2 = 8100 + 8100
c2^2 = 16200
c2 ≈ √16200 ≈ 127.28 ft
Therefore, the length of a throw from the shortstop position to 1st base is approximately 127 ft.