# Right Triangles and Trigonometry Terms

## Get down with the lingo

### 30-60-90 Triangle

A special right triangle where the angles are 30°, 60°, and 90°. In these triangles, the hypotenuse is equal to 2 times the shortest leg, and the long leg equals the shortest leg times the square root of 3. The sides are in the ratio*x*,

*x*√3, 2

*x*.

### 45-45-90 Triangle

A special right triangle where the angles are 45°, 45°, and 90°. In these triangles, both legs are the same length, and the hypotenuse equals the length of the leg times the square root of 2. As was written:*One side to find them all…*. The sides are in the ratio

*x*,

*x*,

*x*√2.

### Geometric Mean

The positive square root of the product of two numbers. Don't let the name fool you; it's actually a super nice guy.### 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*.

### Law Of Sines

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

### 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.### 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.### Solving A Triangle

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