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Flip to reveal answersWhen does the ambiguous case occur?
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All 8 Flashcards — Ambiguous case
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Question
When does the ambiguous case occur?
Answer
Using the sine rule to find an ANGLE (two sides + a non-included angle, SSA).
Question
Why are there two possible angles?
Answer
Because sin θ = sin(180° − θ) — an acute and an obtuse angle share the same sine.
Question
How do you get the second angle?
Answer
Subtract the acute sin⁻¹ value from 180°.
Question
Is finding a side ambiguous?
Answer
No — only finding an angle with the sine rule can give two answers.
Question
Is the cosine rule ambiguous for angles?
Answer
No — cos⁻¹ gives a single angle in 0°–180°.
Question
How do you check if the obtuse triangle is valid?
Answer
Add it to the known angle; keep it only if the total is under 180°.
Question
sin B = 0.6 — find both angles.
Answer
B ≈ 36.9° or 180° − 36.9° = 143.1°.
Question
A = 70°, B = 50° or 130° — which are valid?
Answer
Only 50°, since 70° + 130° = 200° > 180°.
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Topic 3.5 hub
Unit circle & exact values
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