Solving Triangle with A = 40°, B = 60°, c = 10

Trigonometry · Axiom Academy

EXAMPLE Solving Triangles with Law of Sines Find all unknown angles and sides using the given information and trigonometric ratios. Excellent work! You've successfully solved the complete triangle. Here's what we learned: Angle Sum Property: The three angles of any triangle always add up to 180°. Use this to find a missing angle when you know the other two. Law of Sines: The ratio sin(A)/a = sin(B)/b = sin(C)/c holds for any triangle. Use it when you know an angle-side opposite pair. Strategic Setup: Always write the ratio with the known angle-side pair first, then set it equal to the ratio with the unknown side. Reasonableness Check: The largest side should be opposite the largest angle. In our triangle: C (80°) > B (60°) > A (40°), and c (10) > b (8.79) > a (6.53) ✓ Calculator Mode: Always use degree mode when working with angles in degrees! This problem demonstrated an AAS (Angle-Angle-Side) triangle. The Law of Sines is your go-to tool for solving triangles when you know at least one angle-side opposite pair!

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