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Law of Sines and Law of Cosines — a Deeper Look

Question 3 • Precalculus

If all of the side lengths of a triangle had a length of 1, what would the simplified law of sines equation be?

Answer
A
sin A + sin B + sin C = 1
B
sin A = sin B = sin C
C
sin A + 1 = sin B + sin C

Explanation

The law of sines says each side length divided by the sine of its opposite angle is equal: a/sin A = b/sin B = c/sin C. If all three side lengths are 1, this becomes 1/sin A = 1/sin B = 1/sin C, so sin A = sin B = sin C. The correct choice is “sin A = sin B = sin C.”

AI-written and checked against the verified answer.

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