AQA · Mathematics · 8300
GCSE Maths: Trigonometry: sine rule (angles)
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Trigonometry: sine rule (angles) (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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What is the sine rule formula relating sides and angles in 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 used to find a missing angle in a triangle?
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When you know two sides and one angle opposite to one of those sides (e.g., a, b, and angle A).
When can the sine rule be used to find a missing side in a triangle?
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When you know two angles and one side (e.g., angles A and B, and side a or b).
Why might the sine rule give two possible values for an angle?
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Because sin(θ) = sin(180° - θ), so both an acute angle and its supplementary obtuse angle have the same sine value.
What geometric information is needed to apply the sine rule in a real-world bearing problem?
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You need to construct a triangle from the bearing information and identify known sides and angles to use the sine rule.
In an angle of elevation problem involving a vertical object and two ground observers, how can the sine rule help find the height?
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Use the sine rule to find a slant distance from an observer to the top of the object, then use trigonometry (sine) to find the vertical height.
What does 'angle of elevation' mean?
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The angle measured upward from the horizontal to a line of sight toward an object above.
In a bearing and speed problem, how do you find the distance traveled after a given time?
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Distance = speed × time. For example, if speed is 18 km/h and time is 2 hours, distance is 36 km.
What is a bearing in navigation?
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An angle measured clockwise from north, expressed as a three-digit number (e.g., 085°, 152°).
When calculating an upper bound for a length using the sine rule, why must you consider measurement uncertainty?
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Because measurements given to a certain number of significant figures have a range of possible true values, affecting the calculated result.
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