Look at what you know. Two sides and the angle between them: use the cosine rule for the third side, or ½ab sin C for the area. Three sides: use the cosine rule to find an angle.
A side and its opposite angle, plus one more fact: use the sine rule. If the triangle has a right angle, ordinary SOH CAH TOA and Pythagoras are quicker. Some problems need two rules in a row, such as the cosine rule for a side, then the sine rule for an angle.
Worked example
BC = 14 cm, AC = 5 cm and ∠BAC = 66°. Which rule finds ∠ABC?
- BC is opposite the known angle A: a complete opposite pair.
- AC is opposite the angle we want, B.
Answer:the sine rule
Key words
- opposite pair
- a side with its facing angle
- two-step problem
- uses one rule, then another
- SOH CAH TOA
- right-angled trigonometry
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.D.11