// Numbas version: finer_feedback_settings
{"name": "Pythagoras: calculating side length", "extensions": ["eukleides"], "custom_part_types": [], "resources": [["question-resources/Picture1_caMIdF1.png", "Picture1_caMIdF1.png"], ["question-resources/Picture2_6KE4ZpW.png", "Picture2_6KE4ZpW.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Pythagoras: calculating side length", "tags": [], "metadata": {"description": "<p>Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{max_height(25,diagram)}</p>", "advice": "<p><em>Avoid using rounded values in calculations and just round for the final answer.<br/><br/></em>Pythagoras Theorem states that, in a right angled triangle, with hypotenuse $c$:</p>\n<p>\\[a^2 + b^2 = c^2\\]</p>\n<p>Let's call the unknown value $x$,&nbsp;therefore we can write:</p>\n<p><span data-jme-visible=\"{setup}=1\">$a&nbsp;= x$,&nbsp; $b =\\var{ac}$ and $c = \\var{ab}$</span></p>\n<p><span data-jme-visible=\"{setup}=1\">So</span></p>\n<p><span data-jme-visible=\"{setup}=1\">\\[x^2 + \\var{ac}^2 = \\var{ab}^2 \\]</span></p>\n<p><span data-jme-visible=\"{setup}=1\">This is equivalent to </span></p>\n<p><span data-jme-visible=\"{setup}=1\">\\[ \\begin{split} x^2 &amp;= \\var{ab}^2 - \\var{ac}^2 \\\\ &amp;= \\var{ab^2} - \\var{ac^2} \\\\ &amp;= \\var{ab^2-ac^2} \\end{split}\\]</span></p>\n<p><span data-jme-visible=\"{setup}=1\">Therefore,</span></p>\n<p><span data-jme-visible=\"{setup}=1\">\\[ \\begin{split} x &amp;= \\sqrt{\\var{ab^2-ac^2}} \\\\ &amp;= \\var{precround(sqrt(ab^2-ac^2),3)} \\\\ &amp;= \\var{ans} \\text{ (1 d.p.)} \\end{split} \\]</span></p>\n<p></p>\n<p><span data-jme-visible=\"{setup}=2\">$a&nbsp;= \\var{bc}$,&nbsp; $b =\\var{ac}$ and $c = x$</span></p>\n<p><span data-jme-visible=\"{setup}=2\">So</span><br/><br/><span data-jme-visible=\"{setup}=2\">\\[\\var{bc}^2 +&nbsp;\\var{ac}^2 = x^2\\]</span></p>\n<p><span data-jme-visible=\"{setup}=2\">equivalently,</span></p>\n<p><span data-jme-visible=\"{setup}=2\">\\[ \\begin{split} x^2 &amp;=\\var{bc}^2 + \\var{ac}^2 \\\\ &amp;=\\var{bc^2} + \\var{ac^2} \\\\ &amp;=\\var{bc^2 +ac^2} \\end{split}\\]</span></p>\n<p><span data-jme-visible=\"{setup}=2\">Therefore,</span></p>\n<p><span data-jme-visible=\"{setup}=2\">\\[ \\begin{split} x &amp;= \\sqrt{\\var{bc^2 +ac^2}} \\\\ &amp;= \\var{precround(sides_unrounded[2],3)} \\\\ &amp;= \\var{ans} \\text{ (1 d.p.)} \\end{split} \\]</span></p>\n<p></p>\n<p></p>", "rulesets": {}, "extensions": ["eukleides"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"c": {"name": "c", "group": "Unnamed group", "definition": "[random(-5..5 #0.1),random(-5..5 #0.1)]", "description": "", "templateType": "anything", 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