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    "url": "https://numbas.mathcentre.ac.uk/api/questions/12024/?format=api",
    "name": "Apply the cosine rule",
    "published": true,
    "project": "https://numbas.mathcentre.ac.uk/api/projects/601/?format=api",
    "author": {
        "url": "https://numbas.mathcentre.ac.uk/api/users/697/?format=api",
        "profile": "https://numbas.mathcentre.ac.uk/accounts/profile/697/?format=api",
        "full_name": "Newcastle University Mathematics and Statistics",
        "pk": 697,
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    "source": "https://numbas.mathcentre.ac.uk/question/12024/apply-the-cosine-rule.exam?format=api",
    "metadata": {
        "notes": "\n        \t\t<p>I want an obtuse triangle with side lengths $a,b,c$. I need $a^2+b^2&lt;c^2&lt;(a+b)^2$. I start with $c_1=ceil(\\sqrt{a^2+b^2})+1$, $c_2=\\max\\{b+0.9 a, a + 0.9 b\\}$ to establish a range of values for $c$ so that the triangle is neither too flat nor too close to a right-angled triangle. The upper limit ensures that $-\\cos C \\leq 0.9$ and so $\\sin C \\geq 0.435$. Specifying that $a \\leq 11b, b \\leq 11a$ ensures that $\\sin A, \\sin B$ are not too small and thereby ensures that percentage errors are below 0.5%. This last figure points to $a,b \\leq 100$ and there are benefits in $a,b \\geq 10$.&nbsp;</p>\n        \t\t                    <p></p>\n        \t\t",
        "licence": "Creative Commons Attribution 4.0 International",
        "description": "<p>A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).</p>"
    },
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    "resources": []
}