Solve using laws of sine

In solving triangles, when do you use Law of Sines? How about the Law of Cosines? Give at least 2 examples for each.

Use the Law of Sines if: • You know two sides and an angle that is not the angle between the sides. • You know two angles and one side. Use the Law of Cosines if: • You know three sides. • You know two sides and an angle between them. Examples: Solving with the Law of Sines: 1) • ABsin∠C=ACsin∠B\frac{AB}{sin\angle{C}}=\frac{AC}{sin\angle{B}}sin∠CAB​=sin∠BAC​• sin∠B=sin∠C∗ACAB=12∗333=32sin\angle{B}=\frac{sin\angle{C}*AC}{AB} = \frac{\frac{1}{2}*3\sqrt{3}}{3} =\frac{\sqrt{3}}{2}sin∠B=ABsin∠C∗AC​=321​∗33​​=23​​• ∠B=arcsin(sin∠B)=arcsin(32)=60°\angle{B} = arcsin(sin\angle{B}) = arcsin(\frac{\sqrt{3}}{2}) = 60°∠B=arcsin(sin∠B)=arcsin(23​​)=60° • ∠A+∠B+∠C=180°\angle{A} + \angle{B} + \angle{C} = 180°∠A+∠B+∠C=180° • ∠A=180°−∠B−∠C=180°−60°−30°=90°\angle{A} = 180°-\angle{B} - \angle{C} = 180°-60°-30° = 90°∠A=180°−∠B−∠C=180°−60°−30°=90° • ABsin∠C=BCsin∠A\frac{AB}{sin\angle{C}}=\frac{BC}{sin\angle{A}}sin∠CAB​=sin∠ABC​• BC=AB∗sin∠Asin∠C=3∗112=6BC=\frac{AB*sin\angle{A}}{sin\angle{C}}=\frac{3*…

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35 is an outlier

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