Law of Sines and Law of Cosines Quiz – Geometry (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: G-SRT.D.9, G-SRT.D.10, G-SRT.D.11 · Level: Grade 10 Geometry

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What this Solving Any Triangle with Sines, Cosines and Area quiz checks

• Area = ½ab sin C, where C is the angle between sides a and b.
• Law of Sines: sin A / a = sin B / b = sin C / c.
• Law of Cosines: c² = a² + b² − 2ab cos C.
• SSA can produce two different triangles, so check for an obtuse angle.

The 10 questions of the quiz

1. Which formula gives the area of a triangle with sides a and b and included angle C?
2. Two angles and a side that is opposite one of them are known. Which law starts the solution?
3. Which situation calls for the Law of Cosines first?
4. What is the exact area of the triangle?
5. In the Law of Cosines, what does c² = a² + b² − 2ab cos C become when C = 90°?
6. If cos C is negative in the Law of Cosines, angle C is
7. A triangle has A = 50° and B = 60°. What is C?
8. For A = 30°, a = 7, b = 12, why can two triangles exist?
9. Which angle is the largest?
10. Two boats leave a dock on bearings 030° and 100°. What is the angle between their paths?

After the quiz

Missed a question? Reread the Solving Any Triangle with Sines, Cosines and Area lesson, then take the quiz again. Next, solve the Geometry worksheet on Solving Any Triangle with Sines, Cosines and Area, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.

Mis à jour le 22 October 2026