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    "url": "https://numbas.mathcentre.ac.uk/api/questions/12026/?format=api",
    "name": "Apply the cosine rule",
    "published": true,
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        "url": "https://numbas.mathcentre.ac.uk/api/users/697/?format=api",
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        "full_name": "Newcastle University Mathematics and Statistics",
        "pk": 697,
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    "metadata": {
        "notes": "\n        \t\t    \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    \t\t                    <p></p>\n        \t\t    \n        \t\t",
        "licence": "Creative Commons Attribution 4.0 International",
        "description": "<p>A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.</p>"
    },
    "status": null,
    "resources": []
}