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Test: 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.

Question qty: 10
Duration in minutes: 18
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Sample questions

  • Two triangles have equal corresponding sides a and b but different included angles. How can their areas be compared using sine?
  • Triangle sides are a cm, b cm and c cm. Find the angle between the first two sides.
  • Two triangle sides are a cm and b cm, and the sine of their included angle is s. Find the area.
  • Two sides are a cm and b cm, with a 90° included angle. Find the third side.
  • In a triangle, a = a cm, b = b cm and sin A = sa. Find sin B.
  • Two sides and their included angle are known. Which theorem directly finds the third side?
  • Which statement relates triangle side lengths and opposite angles?
  • In a triangle, a = a cm, sin A = sa, and sin B = sb. Find 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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