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KonstantinChe [14]
3 years ago
7

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

irst base.
Mathematics
1 answer:
Archy [21]3 years ago
8 0

Answer:

  70.7 ft

Step-by-step 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

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