Use the law of cosines and the law of sines to solve for all missing parts of triangle ABC when side a = 20, side b = 12, and side c = 14.
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The law of cosines is used when we have
a. three known sides, or
b. two sides and the included angle.
The law of sines is used when we have
- one side and the opposite angle, together with either one angle or one side.
Certain restrictions apply.
first use cosine formula to find an angle and then find other angles by sine formula.
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If you are given three sides, you would use the cosine rule to find TWO of the three angles, and find the third one by subtracting from 180. This is because the sine rule results in ambiguities in certain cases of obtuse angles.
If you absolutely prefer the sine rule (less multiplications) as the second step, you could take precautions as follows:
1. find the angle opposite the longest side (hence the largest angle) by the cosine rule. The angle will be correct whether it is acute or obtuse.
2. find the smallest angle (opposite the shortest side) by the sine rule
3. subtract both from 180 to find the third angle.