How do I use pythagorean theorem if I already know what c is, but I am missing one of the legs?

If you know the length of one of the legs, a (besides the hypotenuse, c), then use
b^2 = c^2 - a^2
and solve for the unknown leg length, b.

This only works IF it is a right triangle.

To use the Pythagorean theorem when you already know the length of the hypotenuse (c) and one of the legs (a), but you're missing the length of the other leg (b), you can follow these steps:

1. Write down the formula: b^2 = c^2 - a^2

2. Substitute the known values of c and a into the formula.

3. Square the values of c and a.

4. Subtract the squared value of a from the squared value of c.

5. Take the square root of the value you just calculated to find the length of the missing leg, b.

Here's an example:

Suppose you have a right triangle with a hypotenuse, c, of length 10 units, and one leg, a, of length 6 units. You want to find the length of the missing leg, b.

Using the formula, b^2 = c^2 - a^2:

b^2 = 10^2 - 6^2


b^2 = 100 - 36

b^2 = 64

Now, take the square root of both sides:

b = √(64)

b = 8 units

Therefore, the missing leg, b, has a length of 8 units.