Free Maths Calculator

Sine and Cosine Rule Calculator

The sine and cosine rules for triangles without a right angle, with the rule chosen by what you know: matching pairs point to the sine rule, two sides and the angle between them point to the cosine rule. The substitution is shown in full before any button maths happens.

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    Worked Example

    In triangle ABC, angle A = 40°, angle B = 70° and b = 8 cm. Find side a.

    1. Sine rule:a ÷ sin A = b ÷ sin B
    2. Rearrange:a = 8 × sin(40°) ÷ sin(70°)
    3. Evaluate:8 × 0.6428 ÷ 0.9397 = 5.472

    Answer: 5.472 cm

    Try These Yourself

    Sides 5, 7 and the angle between them 60°. The opposite side?Show answerHide answer

    Answer: 6.245

    a² = 25 + 49 − 70 × 0.5 = 39.

    All three sides are 6, 8, 10. Find the angle opposite the 10.Show answerHide answer

    Answer: 90°

    cos A = (36 + 64 − 100) ÷ 96 = 0, and cos⁻¹(0) = 90°.