8.2.1: Resources and Key Concepts — Read

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Resources

Law of Cosines: If the angles of a triangle are \(A\), \(B\), and \(C\), and the opposite sides are respectively \(a\), \(b\), and \(c\), then:
- \(a^2 = b^2 + c^2 - 2bc\cos(A)\)
- \(b^2 = a^2 + c^2 - 2ac\cos(B)\)
- \(c^2 = a^2 + b^2 - 2ab\cos(C)\)

Order of Operations: When simplifying the Law of Cosines, follow the order of operations carefully. In an expression like \(b^2 + c^2 - 2bc\cos(A)\), the term \(2bc\cos(A)\) must be calculated before subtracting from the sum of squares. Do not subtract \(2bc\) from \(b^2+c^2\) first.
Incorrectly Applying Law of Sines After Law of Cosines: After using the Law of Cosines to find an angle, you can use the Law of Sines to find a second angle. To avoid the ambiguous case, you should always choose to find the angle opposite the smallest remaining side, as this angle is guaranteed to be acute.

This page titled 8.2.1: Resources and Key Concepts was last modified on Sun, 06 Jul 2025 20:32:39 GMT and is shared under a not declared license and was authored, remixed, and/or curated by Roy Simpson.