Subjects trigonometry

Cosine Sine Law 7B21Bd

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1. The problem is to understand and apply the Law of Cosines or Law of Sines when no angles are given. 2. The Law of Cosines formula is $$c^2 = a^2 + b^2 - 2ab\cos(C)$$ where $a$, $b$, and $c$ are sides of a triangle and $C$ is the angle opposite side $c$. 3. The Law of Sines formula is $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $A$, $B$, and $C$ are angles opposite sides $a$, $b$, and $c$ respectively. 4. Important rule: To use the Law of Sines, you need at least one angle and its opposite side. Without any angles, you cannot use the Law of Sines directly. 5. If no angles are given, use the Law of Cosines to find an angle first by rearranging the formula: $$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$ 6. After finding angle $C$, you can use the Law of Sines to find other angles or sides. 7. Summary: Without any angles, start with the Law of Cosines to find an angle, then use the Law of Sines if needed.