Basic Trigonometry (AQA A-Level Mathematics): Quizzes

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Non-Right-Angled Triangles
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When should you use the Sine Rule to solve a triangle?

When you have two angles and one side

When should you use the Cosine Rule to solve a triangle?

When you have three sides

Which formula represents the Sine Rule?

asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Which formula is the Cosine Rule for finding side cc?

c2=a2+b22abcosCc^2 = a^2 + b^2 - 2ab \cos C

What is the rearranged Cosine Rule for finding angle CC?

cosC=a2+b2c22ab\cos C = \frac{a^2 + b^2 - c^2}{2ab}

What is the area formula for a non-right-angled triangle?

Area=12absinC\text{Area} = \frac{1}{2}ab\sin C

In triangle ABCABC, A=45°\angle A = 45°, B=60°\angle B = 60°, a=7a = 7 cm. Using Sine Rule, find bb (to 2 d.p.)

8.57 cm

In triangle ABCABC, a=5a = 5 cm, b=7b = 7 cm, c=10c = 10 cm. Using Cosine Rule, find C\angle C (to 1 d.p.)

111.5°

In triangle ABCABC, a=8a = 8 cm, b=6b = 6 cm, C=30°\angle C = 30°. Find the area.

12 square cm

You know two sides and the angle between them. Which rule should you use to find the third side?

Cosine Rule

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