We want to find the distance from second base to home plate.
Step 1) Imagine drawing a line from second base to home plate.
If you look to either side of the line, you can see that a triangle is created on both sides. Both triangles are right triangles as well.
Step 2) Determine how you are going to find the length.
Since all the side lengths are the same and the triangles are right triangles, we can use the Pythagorean theorem. Or, because these would be 45-45-90 triangles, we can use that relationship as well. I will demonstrate both ways to solve this problem.
Step 3) 45-45-90 Triangle Relationship
I have attached an image of the 45-45-90 triangle relationship. Hopefully this helps to show this relationship a bit more.
You don't really need to use a calculator here, unless you need the length to a certain decimal place or whole number.
To use this relationship, we know that each side (x on the image) is 90 feet. Using the relationship, we know that then the hypotenuse on the triangle, is 90[tex]\sqrt{2\\}[/tex] feet.
Step 3) Pythagorean Theorem
The Pythagorean Theorem is a^2 + b^2 = c^2. This is another way we can solve this problem.
90^2 + 90^2 = c^2
8100 + 8100 = c^2
16200 = c^2
c = [tex]\sqrt{16200}[/tex] = 90[tex]\sqrt{2\\}[/tex] feet
Hope this helps!! :) If there's anything further to do with this topic that you need help with, please let me know and I'd be happy to help!
