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pythagorean theorem???

im having trouble learning it. i was here learning it and i understoood all of it but then the next day of school i was absent and what they took was an advanced step to learning it.no we have a test tomorrow and its my responsibility to getback on track so i cant ask my teacher. i looked at examples in the book and some how the answers would always come out as a decimal. thats where i get lost. so i put examples and could you please explain each step. thank you!!!! i will give best answer to whoever explains it the best and lets me understand 100% im not slow so it shouldnt be a while for me to understand.

Alright…I’ll try.

First one: Imagine the angle formed between the running path from home to first and first to second. That forms a 90 degree angle.

You WANT to know the distance from home to second. That’s a line segment that passes through the pitchers mound.

A right triangle has been formed between the two basepaths and the imaginary segment from home to 2nd. The basepaths are the LEGS of the right triangle, and the imaginary segment is the HYPOTENUSE (because it is opposite, or across from, the right angle).

Pythagorean theorem says: a^2 + b^2 = c^2. a and b are the lengths of the LEGS, and c is the length of the hypotenuse.

Those basepaths, the LEGS, are 60 feet each. So let’s put those into the formula, square the 60′s, and add.

a^2 + b^2 = c^2
(60)^2 + (60)^2 = c^2
3600 + 3600 = c^2
7200 = c^2

Now, you’re trying to find the value of c…but c is squared in the equation! No worry–take the square root of c^2 to cancel out the exponent. Remember though…if you do that to the left side of the equation you have to do it to the other!

sqrt(7200) = sqrt(c^2)
84.85 = c

That’s the length! Remember, the hypotenuse is always longer than the legs.

Second problem:
Look at that formula again. a^2 + b^2 = c^2

If you plug those numbers into the formula, does it make a true statement? If so, then it IS a right triangle. Let’s check. I’ll put a question mark where the equal sign is until we know if it’s appropriate.

6^2 + 8^2 ? 10^2
36 + 64 ? 100
100 = 100

TRUE! So yes, you have a right triangle.

Sometimes, this doesn’t work. Try 5, 7, and 11.

5^2 + 7^2 ? 11^2
25 + 49 ? 121
74 < 121

This would NOT make a right triangle. As a matter of fact, that less than (<) sign signifies that the triangle will be obtuse (one angle over 90 degrees). A greater than (>) sign would indicate that the triangle is acute (all angles less than 90 degrees).

Good luck on that test!

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