# What are the special rules for 30-60-90 Triangle?

30-60-90 Triangle

In this video you will learn...

• How to identify the short leg,long leg, and the hypothesis
• How to calculate the short leg given the long leg and hypothesis
• How to find the length of tegth of the long leg given the short leg in a 30-60-90 Triangle
• How to find the hypothenuse given the short leg
• Given the long leg of a 30-60-90 triangle how to find the two other legs
Transcript of the video

30=60=90 Triangles
Hi Welcome to MooMooMath. Today we are going to talk about 30-60-90 Triangles. Now there are a set of rules so let me go ahead and share these rules with you, and then we will look at the three different directions that you can use to solve these. The rules for 30-60-90 triangles are as follows. The short leg is always opposite the 30 degree angle. We will call the short leg S. The longer leg is always opposite the 60 degree angle. To find its length takes the short side times the square root of three. Our hypotenuse is always opposite the right angle. To find the hypotenuse take the short leg and multiple it by two. So our short leg is our starting point. Short leg is S Long leg is S times square root of three and hypotenuse is 2 times the short side. Or double the short leg. Let’s go back and work one of these. If we have the short leg all the rules are set. I double it to get the hypotenuse. So I take 2 times 3 so my hypotenuse is 6. Now to get the longer leg I take the short leg times the square root of 3. So I take 3 times the square root of 3 on a calculator or you can leave it as a rational answer. Let’s look at the second method. If given the hypotenuse and you have to figure out the other two sides. The easiest one to get is always the short leg because it is half the hypotenuse. You have a one to two ratio. So if my hypotenuse is 10 then half of that is 5. Once you get the short leg you can get the longer leg, which is the short leg times the square root of three. So it is just five square root three. Now let’s do the hardest direction. When you have the long leg and you’re trying to find the other two sides this is the most difficult direction because you are using the square root of three. Now to go from the short side to long side you multiple by the square root of three. So to go from the long to the short you would divide by the square root of three. So I am taking six divided by the square root of three to get the short leg. To rationalize that multiple the bottom by root three and the top by root three. Square root of three times the square root of three is three. So I have 6 square three over three and the coefficients divide so I have two square root three. Now that is your short leg. You always get the short leg first.  So you double that to get the hypotenuse so two times two is four and the radical stays the same so your hypotenuse is four square root three. So those are your three directions.  Hope this was helpful