Sine law
Use the sine law to find a missing side or angle in an acute triangle, including surveying-style word problems. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
A surveying crew is laying out a triangular park. Angle A = 50deg, angle B = 44deg, and the side opposite angle A is 14 m. Find the length of the side opposite angle B, to one decimal place.
Answer: 12.7
See one solved, step by step
In triangle ABC, angle A = 62deg, side a = 23 m (opposite A), and side b = 24 m (opposite B). Find angle B, to the nearest degree.
📘 Worked solution
1sin(B)/b = sin(A)/a -> sin(B) = b·sin(A)/aRearrange the sine law so the unknown angle's sine is by itself.
2sin(B) = 24·sin(62deg)/23 = 0.9213Substitute the known values.
3B = sin-1(0.9213) = 67.12deg ~ 67degApply inverse sine and round to the nearest degree.
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