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    "url": "https://numbas.mathcentre.ac.uk/api/questions/12027/?format=api",
    "name": "Apply the sine 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/12027/apply-the-sine-rule.exam?format=api",
    "metadata": {
        "notes": "<p>I want acute triangles with side lengths $a,b,c$. I need $|a^2-b^2|&lt;c^2&lt;a^2+b^2$ along with corresponding conditions on $a,b$. In fact the conditions $a^2-b^2&lt;c^2&lt;a^2+b^2$ and $b^2-a^2&lt;c^2&lt;a^2+b^2$ imply also the corresponding conditions on $a,b$. Thus the design of the question involves choosing $a,b$ and then choosing $c$ to meet the required condition. The integer $c$ is chosen randomly between the ceiling of $\\sqrt{|a^2-b^2|}$ and the floor of $\\sqrt{a^2+b^2}$. The first is no greater than the second because $\\max\\{a,b\\}$ lies between them; if $a=b$, then $\\sqrt{a^2+b^2} &gt; 1$. The range of values for $a$ and $b$ may be changed according to taste without invalidating the question, but questions arise about accuracy. My calculations suggest that values of $a,b,c$ between 5 and 100 are safe, but I have been more conservative than that.</p>\n                    <p>The second part tests the ability to apply the same principles as the first part but with a different orientation to the triangle: the first part seeks $b,C,c$ whereas the second seeks $b,A,a$.</p>",
        "licence": "Creative Commons Attribution 4.0 International",
        "description": "<p>Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.</p>"
    },
    "status": "ok",
    "resources": []
}