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Sine and cosine laws
This test applies the sine rule, cosine rule and the trigonometric formula for triangle area. Students select a suitable rule from the given information, calculate sides or angles and assess whether a solution is geometrically valid.
Questions: 10Estimated time: 18 minutes
Time left: 00:00:00
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Sample questions
- Two triangle sides are ___ cm and ___ cm, and the sine of their included angle is ___. Find the area.
- Triangle sides are ___ cm, ___ cm and ___ cm. Find the angle between the first two sides.
- Two sides are ___ cm and ___ cm, with a 90° included angle. Find the third side.
- In a triangle, a = ___ cm, sin A = ___, and sin B = ___. Find b.
- In a triangle, a = ___ cm, b = ___ cm and sin A = ___. Find sin B.
Sine and cosine laws
The sine law a/sin A = b/sin B = c/sin C relates sides to their opposite angles. It is especially useful when one side and its opposite angle are known together with another triangle element.
The cosine law
The cosine law c² = a² + b² − 2ab cos C applies when two sides and their included angle, or all three sides, are known. Always pair a side with its opposite angle. With the sine law, remember that the same sine may correspond to an acute or obtuse angle.
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