AQA · Mathematics · 8300
GCSE Maths: Trigonometry: cosine rule (angles)
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Trigonometry: cosine rule (angles) (Corbettmaths Video 336), 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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When is the cosine rule needed instead of the sine rule?
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When you have two sides and the included angle (SAS) or all three sides (SSS).
To make cos A the subject of a² = b² + c² − 2bc cos A, rearrange to cos A = ?
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(b² + c² − a²) / (2bc)
In a triangle where all three side lengths are known, which form of the cosine rule finds an angle?
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cos A = (b² + c² − a²) / (2bc), the rearranged form.
In a navigation problem where two objects leave from the same point on different bearings, which rule typically finds the distance between them?
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The cosine rule, because you know two distances and the included angle.
What information do you need to find the angle of elevation from a point to an object using the cosine rule?
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Three sides of a triangle formed by the point, the object, and a reference point.
To find the area of a sector when given the radius and chord length, what must you calculate first?
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The angle at the centre, using the cosine rule on the triangle formed by the two radii and the chord.
In a clock problem asking for the distance between hand tips, what angle should you use in the cosine rule?
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The angle between the two hands, calculated from their positions on the clock face.
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