Sine law — find a side
Use the sine law to find a missing side in an acute triangle given two angles and one side. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
In triangle ABC (a model of a triangular park), angle A = 52deg, angle B = 66deg, and side a (opposite angle A) is 14 m. Find the length of side b (opposite angle B), to one decimal place.
a / sin(A) = b / sin(B)
Answer: 16.2
See one solved, step by step
In triangle ABC (a model of a surveyed plot of land), angle A = 36deg, angle B = 61deg, and side a (opposite angle A) is 22 m. Find the length of side b (opposite angle B), to one decimal place.
a / sin(A) = b / sin(B)
📘 Worked solution
1a / sin(A) = b / sin(B)The sine law relates a side to the sine of the angle opposite it — the ratio is the same all around the triangle.
2b = a · sin(B) / sin(A) = 22 · sin(61deg) / sin(36deg)Cross-multiply and isolate b.
3= 22 · 0.8746 / 0.5878Evaluate each sine ratio (calculator in degree mode).
4= 32.7 mDivide to get the length of side b.
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