The Law of Sines is a very useful tool to find an unknown side or angle in a non-right triangle.
The Law of Sines is based on the concept that in a triangle, a large angle will be associated with a long side opposite from it, and a smaller angle will have a shorter side opposite from it.
The Law of Sines is based on these proportional relationships.
Continuing with Example #1: Solving for an unknown angle
Continuing with Example #2: Solving for an unknown side
The correct setup for solving this triangle is:
Recall the Sine function:
When we use the Law of Sines to find an unknown angle, we can run into problems.
Recall that when we solve for an angle, we have to use the Inverse Sine function.
Well, when we do that, the bottom line is we can get multiple answers.
Simple example: If we want to know which angle is represented by Sin(x) = .5
Both 30 degrees and 150 degrees have a Sine value of 0.5
Fortunately, this is easy.
This may or may not be the right answer.
Step 1: Subtract the angle you found from 180 degrees.
180 - 71.805 = 108.195
This is a second possible answer. So, for example, if the other angles in the triangle don't add up to 180 degrees with the first answer, use the 2nd answer.
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