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Course: Precalculus > Unit 2
Lesson 6: Solving general trianglesLaws of sines and cosines review
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.
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 in the following triangle:
According to the law of sines, . Now we can plug the values and solve:
Example 2: Finding a missing angle
Let's find in the following triangle:
According to the law of sines, . 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 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 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 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.
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