Sine law — find an angle
Use the sine law to find a missing angle in a triangle given two sides and one angle. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
In a plot marked out for a community garden ABC, angle A = 52deg. Side a (opposite angle A) is 12 m, and side b (opposite angle B) is 11 m. Find angle B, to the nearest degree.
sin(B) / b = sin(A) / a
Answer: 46
See one solved, step by step
In a triangular field ABC, angle A = 42deg. Side a (opposite angle A) is 13 m, and side b (opposite angle B) is 17 m. Find angle B, to the nearest degree.
sin(B) / b = sin(A) / a
📘 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) = 17 · sin(42deg) / 13 = 0.875Substitute the two known sides and the known angle.
3B = sin-1(0.875) = 61degTake the inverse sine (arcsin) to undo sin() and find the angle.
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