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- Sine rule, cosine rule and area of a triangle
Sine rule, cosine rule and area of a triangle
For triangles without a right angle, use the sine rule, the cosine rule and ½ab sin C.
Sine rule
asin A = bsin B
Use it when you have a matching side and angle pair.
To find an angle, flip it: sin Aa = sin Bb.
Use it when you have a matching side and angle pair.
To find an angle, flip it: sin Aa = sin Bb.
Cosine rule
a2 = b2 + c2 − 2bc cos A
Use it with two sides and the angle between them, or with all three sides to find an angle:
cos A = (b2 + c2 − a2)2bc
Use it with two sides and the angle between them, or with all three sides to find an angle:
cos A = (b2 + c2 − a2)2bc
Area
Area = ½ab sin C, where C is the angle between sides a and b.
In triangle ABC, b = 7 cm, c = 9 cm and A = 50°. Find a.
- a2 = 49 + 81 − 2 × 7 × 9 × cos 50°
- a2 = 130 − 80.99 = 49.01
- a = 7.00 cm
Answer: 7.0 cm
Sine rule for matching side-angle pairs. Cosine rule for two sides and the included angle, or three sides. Area = ½ab sin C.
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