In any triangle, each side divided by the sine of its opposite angle gives the same value: a/sin A = b/sin B = c/sin C. Side a is opposite angle A, and so on.
Use the sine rule when you know a side and its opposite angle, plus one more side or angle. To find a side, put the unknown on top: b = a × sin B / sin A. To find an angle, flip it: sin B = b × sin A / a. If you only know two angles, find the third first, since they add to 180°.
Worked example
∠BAC = 26°, ∠ABC = 65° and BC = 11 cm. Find AC to 1 d.p.
- BC is opposite A and AC is opposite B.
- AC = 11 × sin 65° / sin 26° = 22.74…
Answer:22.7 cm
Key words
- sine rule
- a/sin A = b/sin B = c/sin C
- opposite pair
- a side and the angle facing it
- ambiguous case
- when two different triangles fit the facts
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.D.10, HSG-SRT.D.11