Law of Sines and Law of Cosines
Right-angle trigonometry runs out quickly. The law of sines and the law of cosines handle every other triangle, and the skill is knowing which one a problem calls for.
This quiz covers the SAS and SSS cases that need the law of cosines, the angle-side pairs that suit the law of sines, the SSA ambiguous case that can give two answers, and the area formula.
Every numerical answer was recomputed by hand — two were corrected before publication.
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Sample questions3 of 13 shown
Q1
The Law of Sines states that in any triangle, the ratio of a side to the sine of its opposite angle is constant. Which formula correctly represents this?
Q2
When should you use the Law of Cosines instead of the Law of Sines?
Q3
In a triangle, you know a = 5, b = 7, and angle C = 60°. Which law would you use first to find side c?
What This Quiz Covers
- The law of sines and when it applies
- The law of cosines for SAS and SSS
- The SSA ambiguous case
- Which cases determine a unique triangle
- Area from two sides and the included angle
- Heron's formula
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