AQA · Mathematics · 8300
GCSE Maths: Trigonometry: cosine rule (sides)
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Trigonometry: cosine rule (sides) (Corbettmaths Video 335), 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 cosine rule formula for finding side a?
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a² = b² + c² − 2bc cos A
When should you use the cosine rule instead of the sine rule?
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When you know two sides and the included angle (SAS), or when you know all three sides (SSS) and need to find an angle.
If you rearrange a² = b² + c² − 2bc cos A to make cos A the subject, what is the result?
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cos A = (b² + c² − a²) / (2bc)
Why can the cosine rule be used to find distances between two boats when given their distances and bearings from a lighthouse?
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The lighthouse and two boats form a triangle where two sides (distances from lighthouse) and the included angle (difference in bearings) are known (SAS).
To find the smallest angle in a triangle using the cosine rule, which side should you use?
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The smallest angle is opposite the shortest side.
In a triangle with vertices at points A and B on the ground and a balloon in the air, what triangle property allows you to use the cosine rule?
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The three distances (A to balloon, B to balloon, and A to B) form a triangle where all three sides can be known or calculated.
How can you find the angle at the center of a sector when you know the radius and chord length?
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Use the cosine rule on the triangle formed by the two radii and the chord (SSS configuration).
To solve a quadrilateral problem using the cosine rule, what is a common first step?
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Divide the quadrilateral into triangles by drawing a diagonal, then apply the cosine rule to those triangles.
For a clock with a minute hand of length m and hour hand of length h, what information do you need to find the distance between the tips?
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The angle between the two hands at the given time, then use the cosine rule with the two hand lengths and included angle.
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