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MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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6.5 The Law of Sines

Focus on law of sines and ambiguous case.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Law of Sines: finding a side (ASA/AAS)Worked steps · five questions02The ambiguous case (SSA)Worked steps · five questions03Applications of the Law of SinesWorked steps · five questions
Lesson brief and rules

6.5 The Law of Sines

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} for a triangle.

Worked example 11
01 / In a triangle, A=30∘,B=90∘A=30^{\circ}, B=90^{\circ}, side a=4a=4. Find side bb.
02 / asin⁡30∘=bsin⁡90∘\dfrac{a}{\sin 30^{\circ}}=\dfrac{b}{\sin 90^{\circ}}. b=4⋅112=8b=4\cdot \dfrac{1}{\dfrac{1}{2}}=8.
03 / Answer: 88
Worked example 2 · Ambiguous case

With two sides and a nonincluded angle, how many triangles might SSASSA determine?

The SSASSA case can have no, one, or two solutions depending on the lengths and angle. Answer: 0,10, 1, or 22

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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