Use the Law of Cosines to find the remaining side(s) and angle(s) if possible. a=7, b=10, c=13

Name: Problem 6, Chapter 11: Precalculus
Uploaded: 2021-08-18T17:48:58-08:00
Duration: 3 min 25 s
Channel: Allison Knapp
Description: Use the Law of Cosines to find the remaining side(s) and angle(s) if possible. a=7, b=10, c=13

step 1 So in this problem we are asked to solve for, or solve the triangles. We're solving for these th

Use the Law of Cosines to find the remaining side(s) and...

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Key Concepts

Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that the interior angles of any triangle always add up to 180 degrees. This important principle is used to find an unknown angle when the other angles are known, ensuring the consistency and correctness of the triangle’s geometry.

Solving Triangles with SSS Information

When all three sides of a triangle are given (the Side-Side-Side or SSS case), solving the triangle means finding all its interior angles. This is typically done by applying the Law of Cosines to determine each angle, and then using the Triangle Angle Sum Theorem to check that the computed angles sum to 180 degrees. This method is a crucial tool in the study of oblique triangles where no right angle exists.

Law of Cosines

The Law of Cosines is a fundamental trigonometric relation that connects the three sides of a triangle with one of its angles. It extends the Pythagorean theorem to any triangle by taking into account the non-right angles, and is typically written as c² = a² + b² - 2ab cos(?), where ? is the angle opposite side c. This formula allows one to determine an unknown side when two sides and their included angle are known, or to calculate an unknown angle when all three sides are provided.

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