AQA · Mathematics · 8300
GCSE Maths: Trigonometry: sine rule (sides)
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Trigonometry: sine rule (sides) (Corbettmaths Video 333), 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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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 to angles A, B, C respectively.
When can the sine rule be applied to a triangle?
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When you know either: (1) two angles and one side, or (2) two sides and a non-included angle.
Why can the sine rule sometimes give two possible values for an unknown angle?
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Because sin(θ) = sin(180° - θ), so an angle and its supplement have the same sine value. This is called the ambiguous case.
What trigonometric equation results from rearranging the sine rule to solve for an unknown side a?
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a = (b × sin(A)) / sin(B), where b is a known side, A is the angle opposite side a, and B is the angle opposite side b.
What trigonometric equation results from rearranging the sine rule to solve for an unknown angle A?
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sin(A) = (a × sin(B)) / b, where a is the side opposite angle A, b is a known side, and B is the angle opposite side b.
In a bearing problem where two objects leave from the same point at different bearings, what geometric shape is formed?
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A triangle, where the angle between the two paths can be found from the difference in bearings.
In an angle of elevation problem with two observers at different points, what role does the sine rule play?
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It helps find unknown sides or heights by relating the angles of elevation to the distances between observers and the object.
When applying the sine rule to a triangle with measurements given to significant figures, how do you find the upper bound for a calculated side?
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Use the upper bounds of the given sides and the bounds of angles that make the result largest, then apply the sine rule.
What strategy is needed to solve a composite geometry problem where a triangle contains an internal point?
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Break the problem into smaller triangles, apply the sine rule to each part sequentially, and use results from one triangle as inputs for the next.
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