## Related questions with answers

Question

Alejandro said the Law of Sines always gives one answer. Explain and correct Alejandro's error.

Solution

VerifiedThe law of sines gives one answer except in the ambiguous case when we are given the lengths of two sides and the measure of a non included angle it gives two answers because $\sin \theta=\sin 180\text{\textdegree}-\theta$

Then the law of sines in this case gives one acute angle in the 1st quadrant and one obtuse angle in the 2nd quadrant.

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