AQA · Mathematics · 8300
GCSE Maths: Trigonometry: sine rule (ambiguous case)
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Trigonometry: sine rule (ambiguous case) (Corbettmaths Video 334), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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In what type of triangle problem does the sine rule ambiguous case arise?
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When you know two sides and an angle opposite one of them (SSA configuration), there may be zero, one, or two possible triangles.
When using the sine rule to find an unknown angle, why might two different angle values satisfy the equation?
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Because sin(θ) = sin(180° - θ), both an acute angle and its supplementary obtuse angle have the same sine value.
What is the sine rule formula relating sides and angles of a triangle?
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a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are sides opposite angles A, B, C respectively.
When applying the sine rule in a real-world bearing problem, what must you first do with the bearing angles?
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Convert the bearings to angles within the triangle by using geometric relationships (e.g., alternate angles, angle sum).
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