Distributing the Pythagorean Theorem 
The use of the Pythagorean theorom involves three variables, A, B, and C. C is always the hypotenuse.
A and B are the two legs. Using the information from the Introduction section, we can rewrite the hypotenuse
equals the square root of the Vertical Leg2 + the Horizontal Leg2 as A2 + B2 = C2. Using the distributive property,
we can also rewrite A2 + B2 = C2 as C2 - A2 = B2 or C2 - B2 = A2. Let's try some examples.
Example 1.1
Find the hypotenuse's length.
To Find the Hypotenuse (C) we need to use the formula A2 + B2 = C2.
22 is 4. 32 is 9. We add 4 and 9, we get 13.
Then, we need to get the square root of 13.
The square root of 13 is 3.6055512.
Therefore, the hypotenuse of the above triangle has a length of 3.6055512.
Example 1.2
Find the Horizontal leg's length.
To Find the Horizontal Leg (A) we need to use the formula C2 - B2 = A2.
42 is 16. 52 is 25. We subtract 16 from 25, we get 9.
Then, we need to get the square root of 9.
The square root of 9 is 3.
Therefore, the horizontal leg of the above triangle has a length of 3.
Example 1.3
Find the vertical leg's length.
To Find the Vertical Leg (B) we need to use the formula C2 - A2 = B2.
72 is 49. 82 is 64. We subtract 49 from 64, we get 15.
Then, we need to get the square root of 15.
The square root of 15 is 3.8729833.
Therefore, the vertical leg of the above triangle has a length of 3.8729833.
How do you know that this is true? If you are curious to find out go to the Proofs section.
