How do i do the pythagorean theream

The Pythagorean Theorem states that: a^2+b^2=c^2
a and b are two of the triangles sides, while c is the hypotenuse (the longest side).

For example: #1 
a^2+17^2=41^2
a^2+289=1681
a^2=1392
sqrt(a^2)=sqrt(1392)
a=4sqrt(87)

The Pythagorean Theorem goes by the formula a^2+b^2=c^2, where a and b are triangle legs (the sides that form a 90-degree angle), and c is the hypotenuse (the longest side on top). Let's do #6 for an example.

#6 gives us side lengths 22 and 47. To find the third length (c/the hypotenuse), square 22 and 47, then add them to get you 2693. We then find the square root of this (because this is c and not c^2) to get an approximate answer of 51.89.

But what happens when you only have the hypotenuse and one side length? Here's what you do (We'll use #5).

You know that a^2+b^2=c^2. You have c (the hypotenuse) and a or b (whichever variable would work unless otherwise specified). Using #5, we see that 42^2+b^2=128^2. Simplifying this, we get that 1764+b^2=16384. This means that (when simplified) b^2=16384-1764, which is 14620. We're not done though! We see that b^2=14620, not b by itself. We can find b by finding the square root of 14620, which is 120.91.

Hope this helps; if you need help, feel free to ask questions!

:)