Question

at the local baseball diamond,the distance from home base to second base is 100 feet. Determine the distance from home base to first base.

Answer 1

70.7 ft

Explanation:

The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.

___

For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...

hypotenuse = √(side² + side²) = √(1²+1²) = √2

Then the diamond distances satisfy the proportion ...

hypotenuse/side = 100 ft/(base distance) = √2/1

or ...

base distance = (100 ft)/√2 ≈ 70.71068 ft