Question

a baseball diamond is a square with sides that are 27.4 m. the pitchers mound is 18.4m from homeplate on the line joining hommeplate and second base. how far is it from the pitchars mound to first base

Answer 1

19.4 m

Explanation:

The law of cosines can be used to figure this. The angle between the line to the pitcher's mound and the first-base line is 45°, so the distance (d) from the mound to first can be found from ...

d² = 18.4² +27.4² -2·18.4·27.4·cos(45°) ≈ 376.33

d ≈ √376.33 ≈ 19.4 . . . . meters

It is about 19.4 meters from the pitcher's mound to first base.

Answer 2

The diagonal of the diamond measures
d = 27.4 √2
Half of this is
d/2 = 12.35 √2

The distance from the center of the diamond to the pitchers mound is
h = 18.4 - 12.35 √2

Using Pythagorean theorem
x² = (d/2)² + h²
substituting and solving for x gives the distance between the pitchers mound and the second base