How To: Find Leg Lengths and Hypotenuse of a 45 45 90 Triangle

A 45 45 90 triangle is a special right triangle because you can use short cuts to find leg length and hypotenuse length. This video solves two problems involving leg length and hypotenuse length.

Highlights of the video

A 45-45-90 triangle is an isosceles triangle, which means two sides are the same, has a right angle.

The angles, the two acute angles are two 45 degree angles, and are congruent.

You can solve a 45 45 90 triangle with one side because there are some special rules.

Let's look at the rules for 45- 45 -90. If you know one leg you know the other leg because these are isosceles, and the two sides are the same.

There is a ratio that all you need to do is take one of the legs and multiple by the square root of two to get the length of the hypotenuse.

The two legs of a 45 45 90 are the same, and two times the square root two gives us the length of the hypotenuse.

If we know this leg is 7 then the other leg is 7 because it is isosceles and the ratio says I just multiple this 7 times the square root of 2 to get the hypotenuse.

What if you don't know the two legs but you do know the hypotenuse.

Since the rule is you take the leg times square root 2 to go from the leg to the hypotenuse, to get the hypotenuse just reverse the operation and divide by the square root of two.

I will take 12 and divide it by the square root of two. You can't have a square root on the bottom of a fraction so I'm going to rationalize that by the factor of one so I have square root of two over square root of two, that's really just one.

The square root of two times square root of two is equal to the square root of four, which is two. Now on the top I have twelve times the square root of two.

I can't multiple these together so I just stick them next to each other ,and then let's divide these outside coefficients, which is 12 divided by 2, which is 6 and that simplifies to 6 root two.

So that means each leg is 6 square root two.

In summary, to get hypotenuse you multiple by square root of two and to get leg length you divide by the square of two.