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Using the Pythagorean Theorem to find a Missing Leg - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The legs of a right triangle are the sides that are adjacent to its right angle. Sometimes we have problems that ask us to find a missing length of one of these legs. We can use the Pythagorean theorem to find a missing leg of a triangle, but only if we know the length measure of the hypotenuse and the other one of the legs.

The Pythagorean Theorem only applies to a right triangle. And in that right triangle we can say that the legs a and b that is those sides that are adjacent to this right angle. If I square them and add them up it's going to equal your hypotenuse squared or c squared so your hypotenuse remember is that side that is opposite your 90 degree angle and since the triangle angle sum says that if this is 90 degrees then both of these angles have to be less than 90, your hypotenuse will always be the longest side in a right triangle.
Let's say you knew one of your legs and your hypotenuse, so let's say you knew a and you knew c you would solve for your missing leg by squaring a, squaring c and then you're going to have to subtract a squared whatever it is. So that's going to be an a not a 2, an a squared so you're going to get b squared is equal to c squared minus a squared. And then to solve you're going to have to take the square root of both sides. So b is going to equal the square root of c squared minus a squared sum number. So it's a little more involved when you know 1 leg and your hypotenuse and you're trying to solve for the other leg. You're going to have to subtract and then take the square root.

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