Sine, Cosine Rule & Area of TrianglesCambridge IGCSE Maths: Flashcards

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State the sine rule.

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State the sine rule.: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
State the cosine rule (side version).: $a^2 = b^2 + c^2 - 2bc\cos A$
State the rearranged cosine rule for finding an angle.: $\cos A = \frac{b^2+c^2-a^2}{2bc}$
State the formula for the area of a triangle using two sides and an included angle.: $\text{Area} = \frac{1}{2}ab\sin C$
When should you use the sine rule?: When you know a matching angle-side pair, plus one other side or angle
When should you use the cosine rule?: When you know two sides and the included angle, or all three sides
What is the 'ambiguous case' in trigonometry?: A situation using the sine rule where two different triangles both fit the given data — one with an acute angle, one with the obtuse supplement
Why doesn't the cosine rule suffer from the ambiguous case?: Because cosine is negative for obtuse angles and positive for acute ones, so it directly identifies which type of angle it is
Triangle sides $b=5$ , $c=8$ , included angle $A=70°$ . Find the area.: Area $= \frac{1}{2}(5)(8)\sin70° \approx 18.8$
What does 'included angle' mean?: The angle formed between two specific given sides of a triangle
A triangle has $A=35°$ , $a=6$ , $b=9$ . Which rule finds angle $B$ ?: The sine rule, using $\frac{\sin B}{b} = \frac{\sin A}{a}$
What sense-check should you always apply to any solved triangle?: Check that the three angles sum to 180°