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G-SRT.10 Warmup M3-042-A05-V01

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

Use the Law of Cosines to find a missing side from two sides and the included angle

Problem

In the triangle shown, \(a~=~7\), \(b~=~9\), and the included angle \(C~=~60°\). Use the Law of Cosines to find side \(c\).

A scale-faithful SAS triangle marking two known sides, their included angle, and the unknown opposite side. Open full size
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What this problem is really about

With two sides and their included angle, match the unknown side to the angle opposite it and use the corresponding Law of Cosines form. Evaluate the cosine correction carefully, then take the positive square root because a side length cannot be negative. Preserve the exact radical unless a decimal is specifically requested.

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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
Use the Law of Cosines to find a missing side from two sides and the included angle