# Right Triangles and Trigonometry Terms

## Get down with the lingo

### Geometric Mean

The*n*th root of the product of

*n*numbers. That's not so mean, is it?

### Pythagorean Triple

A right triangle whose three side lengths are all integers. For instance, a triangle with side lengths of 3, 4, and 5 would be considered a Pythagorean triple.### Pythagorean Theorem

States that in any right triangle, the sum of the lengths of the legs squared equals the square of the length of the hypotenuse. More simply,*a*

^{2}+

*b*

^{2}=

*c*

^{2}.

### 45-45-90 Triangle

### 30-60-90 Triangle

### Trigonometry

The use of a triangle's angles and side lengths to calculate its angles and side lengths. It seems kind of redundant, but it's not.### Trigonometric Ratios

Specific fractions made by dividing specific side lengths. The three main ones to remember are sine, cosine, and tangent. The**sine**of an angle is the side length opposite the angle over the hypotenuse. The

**cosine**is the adjacent side over the hypotenuse. The

**tangent**is the opposite side over the adjacent side. Capisce?

### Law Of Sines

A relationship stating that in any non-right triangle, the sine of any angle divided by its opposite side equals the sine of another angle divided by its opposite side. In other words,### Solving A Triangle

Finding all the side lengths and angle measures in a triangle. At least there are only three of each.### SOHCAHTOA

What you should do after stubbing your toe. Also, a mnemonic for remembering the three main trig ratios: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. Now go get some ice because that thing's gonna bruise.### Law Of Cosines

A relationship between the angles and side lengths of a triangle, stating that the square of any side length equals the sum of the squares of the two other side lengths minus two times the product of the two other side lengths and the cosine of the opposite angle. Basically, this:*a*

^{2}=

*b*

^{2}+

*c*

^{2}– 2

*bc*cos

*A*.

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