# Laws of sines and cosines review

CCSS Math: HSG.SRT.D.10, HSG.SRT.D.11

Review the law of sines and the law of cosines, and use them to solve problems with any triangle.

## Law of sines

## Law of cosines

*Want to learn more about the law of sines? Check out this video.*

*Want to learn more about the law of cosines? Check out this video.*

## Practice set 1: Solving triangles using the law of sines

This law is useful for finding a missing angle when given an angle and two sides, or for finding a missing side when given two angles and one side.

### Example 1: Finding a missing side

Let's find $AC$ in the following triangle:

According to the law of sines, $\dfrac{AB}{\sin(\angle C)}=\dfrac{AC}{\sin(\angle B)}$. Now we can plug the values and solve:

### Example 2: Finding a missing angle

Let's find $m\angle A$ in the following triangle:

According to the law of sines, $\dfrac{BC}{\sin(\angle A)}=\dfrac{AB}{\sin(\angle C)}$. Now we can plug the values and solve:

Evaluating using the calculator and rounding:

Remember that if the missing angle is obtuse, we need to take $180^\circ$ and subtract what we got from the calculator.

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

## Practice set 2: Solving triangles using the law of cosines

This law is mostly useful for finding an angle measure when given all side lengths. It's also useful for finding a missing side when given the other sides and one angle measure.

### Example 1: Finding an angle

Let's find $m\angle B$ in the following triangle:

According to the law of cosines:

Now we can plug the values and solve:

Evaluating using the calculator and rounding:

### Example 2: Finding a missing side

Let's find $AB$ in the following triangle:

According to the law of cosines:

Now we can plug the values and solve:

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

## Practice set 3: General triangle word problems

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