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G-SRT.10 Warmup M3-042-A07-V01

Prove the Laws of Sines and Cosines and use them to solve problems.

Choose whether to use the Law of Sines or the Law of Cosines first

Problem

The triangle shown gives \(ASA\) or \(AAS\) information and a known side-opposite-angle pair. Name the law to use first.

A genuine triangle marking exactly the two angles + opposite pair information without naming the solving law. Open full size
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What this problem is really about

Inventory the given triangle information before deciding on a law. A known side with its opposite angle creates the proportion structure used by the Law of Sines, while three sides or two sides with their included angle point to the Law of Cosines. Match the data pattern first, then write the corresponding relationship.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
G-SRT.10
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Prove the Laws of Sines and Cosines and use them to solve problems.
Problem type
Choose whether to use the Law of Sines or the Law of Cosines first