# Right triangle trigonometry review

CCSS Math: HSG.SRT.C.8

Review right triangle trigonometry and how to use it to solve problems.

## What are the basic trigonometric ratios?

$\large\sin(\angle A)=$ | $\large\dfrac{\blueD{\text{opposite}}}{\goldD{\text{hypotenuse}}}$ | |

$\large\cos(\angle A)=$ | $\large\dfrac{\purpleC{\text{adjacent}}}{\goldD{\text{hypotenuse}}}$ | |

$\large\tan(\angle A)=$ | $\large\dfrac{\blueD{\text{opposite}}}{\purpleC{\text{adjacent}}}$ |

*Want to learn more about sine, cosine, and tangent? Check out this video.*

## Practice set 1: Solving for a side

Trigonometry can be used to find a missing side length in a right triangle. Let's find, for example, the measure of $AC$ in this triangle:

We are given the measure of angle $\angle B$ and the length of the $\goldD{\text{hypotenuse}}$, and we are asked to find the side $\blueD{\text{opposite}}$ to $\angle B$. The trigonometric ratio that contains both of those sides is the sine:

Now we evaluate using the calculator and round:

*Want to try more problems like this? Check out this exercise.*

## Practice set 2: Solving for an angle

Trigonometry can also be used to find missing angle measures. Let's find, for example, the measure of $\angle A$ in this triangle:

We are given the length of the side $\purpleC{\text{adjacent}}$ to the missing angle, and the length of the $\goldD{\text{hypotenuse}}$. The trigonometric ratio that contains both of those sides is the cosine:

Now we evaluate using the calculator and round:

*Want to try more problems like this? Check out this exercise.*

## Practice set 3: Right triangle word problems

*Want to try more problems like this? Check out this exercise.*