Answer:
the diagonal of this right triangle, which is the distance from first base to third base, is equal to the square root of 2 times the length of one of the legs, or 90√2ft.
Explanation:
The distance from first base to third base in a baseball diamond is the diagonal of a square with side length 90ft. This is a special right triangle, known as a 45-45-90 triangle. The Pythagorean Theorem tells us that the diagonal of a 45-45-90 triangle is equal to the square root of 2 times the length of one of the legs.
Therefore, the distance from first base to third base in a baseball diamond is:
sqrt(2) * 90ft = 90sqrt(2)ft
This can be simplified to 90√2ft in simplest radical form.
Another way to think about this problem is to imagine that you are standing on first base and looking towards third base. The pitcher's mound is directly in between the two bases. If you draw a line from first base to third base, it will form a right triangle with the pitcher's mound as the right angle. The two legs of this right triangle are both 90ft long, because the distance from first base to the pitcher's mound is 90ft and the distance from the pitcher's mound to third base is also 90ft.