// Numbas version: exam_results_page_options
{"name": "Right angled triangles: SOHCAHTOA 2 - find side", "extensions": ["eukleides"], "custom_part_types": [], "resources": [["question-resources/Picture1_caMIdF1.png", "/srv/numbas/media/question-resources/Picture1_caMIdF1.png"], ["question-resources/Picture2_6KE4ZpW.png", "/srv/numbas/media/question-resources/Picture2_6KE4ZpW.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Right angled triangles: SOHCAHTOA 2 - find side", "tags": [], "metadata": {"description": "<p>Draws a triangle based on 3 side lengths.&nbsp; Randomises asking angle or side.</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>{advice}</p>", "rulesets": {}, "extensions": ["eukleides"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ab": {"name": "ab", "group": "Unnamed group", "definition": "random(7..12)", "description": "", "templateType": "anything", "can_override": false}, "ac": {"name": "ac", "group": "Unnamed group", "definition": "precround(ab*cos(pi*angle/180),2)", "description": "", "templateType": "anything", "can_override": false}, "bc": {"name": "bc", "group": "Unnamed group", "definition": "precround(ab*sin(pi*angle/180),2)", "description": "", "templateType": "anything", "can_override": false}, "d_t_s_1": {"name": "d_t_s_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label(angle)\n    , b..c label(bc)\n    , a..c label('x')\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_c_s_1": {"name": "d_c_s_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label(angle)\n    , a..c label('x')\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "diagram": {"name": "diagram", "group": "Unnamed group", "definition": "if(SCT='s',\n  if(AngORside='ang',\n    random(d_s_a_1,d_s_a_2),\n    random(d_s_s_1,d_s_s_2)),\n  if(SCT='t',\n     if(AngORside='ang',\n    random(d_t_a_1,d_t_a_2),\n    random(d_t_s_1,d_t_s_2)),\n  if(SCT='c',\n     if(AngORside='ang',\n    random(d_c_a_1,d_c_a_2),\n    random(d_c_s_1,d_c_s_2)),'X')))\n   ", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "Unnamed group", "definition": "random(32..72)", "description": "", "templateType": "anything", "can_override": false}, "d_s_s_1": {"name": "d_s_s_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label(angle)\n    , b..c label('x')\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_c_a_1": {"name": "d_c_a_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label('x')\n    , a..c label(ac)\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_s_a_1": {"name": "d_s_a_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label('x')\n    , b..c label(bc)\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_t_a_1": {"name": "d_t_a_1", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label('x')\n    , b..c label(bc)\n    , a..c label(ac)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_t_s_2": {"name": "d_t_s_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,-ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(b,a,c) label(angle)\n    , b..c label(bc)\n    , a..c label('x')\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_c_a_2": {"name": "d_c_a_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,-ac),\n    b, point(bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(b,a,c) label('x')\n    , a..c label(ac)\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "SCT": {"name": "SCT", "group": "Unnamed group", "definition": "random('s','c','t')", "description": "", "templateType": "anything", "can_override": false}, "AngORside": {"name": "AngORside", "group": "Unnamed group", "definition": "'side'", "description": "", "templateType": "anything", "can_override": false}, "d_c_s_2": {"name": "d_c_s_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(-bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(b,a,c) label(angle)\n    , a..c label('x')\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_s_a_2": {"name": "d_s_a_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,-ac),\n    b, point(-bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label('x')\n    , b..c label(bc)\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_s_s_2": {"name": "d_s_s_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,-ac),\n    b, point(-bc,0),\n    c, point(0,0),\n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(c,a,b) label(angle)\n    , b..c label('x')\n    , a..b label(ab)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "d_t_a_2": {"name": "d_t_a_2", "group": "triangle types", "definition": "eukleides(\"A right-angled triangle\",\n  let(\n    a, point(0,ac),\n    b, point(-bc,0),\n    c, point(0,0), \n\n    [\n    \n     a..b..c\n    , angle(a,c,b) right\n    , angle(b,a,c) label('x')\n    , b..c label(bc)\n    , a..c label(ac)\n    \n    ]\n  ),\n[\"angle\":{angle}]\n)", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Unnamed group", "definition": "if(SCT='s',\n  if(AngORside='ang',\n    angle,\n    bc),\n  if(SCT='t',\n     if(AngORside='ang',\n    angle,\n    ac),\n     if(AngORside='ang',\n    angle,ac)))", "description": "", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "advice", "definition": "if(SCT='s',\n  if(AngORside='ang',\n    {sin_a},\n    {sin_bc}),\n  if(SCT='c',\n     if(AngORside='ang',\n    {cos_a},\n    {cos_ac}),\n     if(AngORside='ang',\n    {tan_a},{tan_ac})))", "description": "", "templateType": "anything", "can_override": false}, "sin_a": {"name": "sin_a", "group": "advice", "definition": "\"<p>In this situation $x$ is an angle. &nbsp;We label the known sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we are interested in:</p>\\n<p>$Opposite = \\\\var{bc}$<br />$Hyptonuse = \\\\var{ab}$<br /><br />We have \\'O\\' and \\'H\\' in <strong>SOH</strong>CAHTOA, so we know we need to use the $sin$ formula:</p>\\n<p>\\\\[ sin(Angle) = \\\\frac{Opposite}{Hypotenuse}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ sin(x) = \\\\frac{\\\\var{bc}}{\\\\var{ab}}\\\\]<br /><br />We need to use the \\'inverse sin\\' button on the calculator (also called $arcsin$ or notated&nbsp;$sin^{-1}$) in order to isolate $x$:<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = arcsin(\\\\var{bc}/\\\\var{ab})\\\\]</p>\\n<p>\\\\[ x = \\\\var{precround(180*(arcsin(bc/(ab)))/pi,4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[x = \\\\var{precround(180*(arcsin(bc/(ab)))/pi,2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "cos_a": {"name": "cos_a", "group": "advice", "definition": "\"<p>In this situation $x$ is an angle. &nbsp;We label the known sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we are interested in:</p>\\n<p>$Adjacent = \\\\var{ac}$<br />$Hyptonuse = \\\\var{ab}$<br /><br />We have \\'A\\' and \\'H\\' in SOH<strong>CAH</strong>TOA, so we know we need to use the $cos$ formula:</p>\\n<p>\\\\[ cos(Angle) = \\\\frac{Adjacent}{Hypotenuse}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ cos(x) = \\\\frac{\\\\var{ac}}{\\\\var{ab}}\\\\]<br /><br />We need to use the \\'inverse cos\\' button on the calculator (also called $arccos$ or notated&nbsp;$cos^{-1}$) in order to isolate $x$:<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = arccos(\\\\var{ac}/\\\\var{ab})\\\\]</p>\\n<p>\\\\[ x = \\\\var{precround(180*(arccos(ac/(ab)))/pi,4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[x = \\\\var{precround(180*(arccos(ac/(ab)))/pi,2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "tan_a": {"name": "tan_a", "group": "advice", "definition": "\"<p>In this situation $x$ is an angle. &nbsp;We label the known sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we are interested in:</p>\\n<p>$Opposite = \\\\var{bc}$<br />$Adjacent = \\\\var{ac}$<br /><br />We have \\'O\\' and \\'A\\' in SOHCAH<strong>TOA</strong>, so we know we need to use the $tan$ formula:</p>\\n<p>\\\\[ tan(Angle) = \\\\frac{Opposite}{Adjacent}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ tan(x) = \\\\frac{\\\\var{bc}}{\\\\var{ac}}\\\\]<br /><br />We need to use the \\'inverse sin\\' button on the calculator (also called $arctan$ or notated&nbsp;$tan^{-1}$) in order to isolate $x$:<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = arctan(\\\\var{bc}/\\\\var{ac})\\\\]</p>\\n<p>\\\\[ x = \\\\var{precround(180*(arctan(bc/(ac)))/pi,4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[x = \\\\var{precround(180*(arctan(bc/(ac)))/pi,2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "sin_bc": {"name": "sin_bc", "group": "advice", "definition": "\"<p>In this situation $x$ is a&nbsp;side. &nbsp;We label the relevant&nbsp;sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we know:</p>\\n<p>$Opposite = x$<br />$Hypotenuse = \\\\var{ab}$<br /><br />We have \\'O\\' and \\'H\\' in <strong>SOH</strong>CAHTOA, so we know we need to use the $sin$ formula:</p>\\n<p>\\\\[ sin(Angle) = \\\\frac{Opposite}{Hypotenuse}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ sin(\\\\var{angle}) = \\\\frac{x}{\\\\var{ab}}\\\\]<br /><br />and rearrange to give:</p>\\n<p>\\\\[ x = \\\\var{ab} \\\\times \\\\sin(\\\\var{angle}) \\\\]<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = \\\\var{precround(ab*sin(pi*angle/180),4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[ x = \\\\var{precround(ab*sin(pi*angle/180),2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "cos_ac": {"name": "cos_ac", "group": "advice", "definition": "\"<p>In this situation $x$ is a&nbsp;side. &nbsp;We label the relevant&nbsp;sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we know:</p>\\n<p>$Hypotenuse = \\\\var{ab}$<br />$Adjacent = x$<br /><br />We have \\'A\\' and \\'H\\' in SOH<strong>CAH</strong>TOA, so we know we need to use the $cos$ formula:</p>\\n<p></p>\\n<p>\\\\[ cos(Angle) = \\\\frac{Adjacent}{Hypotenuse}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ cos(\\\\var{angle}) = \\\\frac{x}{\\\\var{ab}}\\\\]<br /><br />and rearrange to give:</p>\\n<p>\\\\[ x = \\\\var{ab} \\\\times \\\\cos(\\\\var{angle}) \\\\]<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = \\\\var{precround(ab*cos(pi*angle/180),4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[ x = \\\\var{precround(ab*cos(pi*angle/180),2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "tan_ac": {"name": "tan_ac", "group": "advice", "definition": "\"<p>In this situation $x$ is a&nbsp;side. &nbsp;We label the relevant&nbsp;sides of the triangle \\'opposite\\', \\'adjacent\\' and \\'hypothenuse\\' in relation to the angle we know:</p>\\n<p>$Opposite = \\\\var{bc}$<br />$Adjacent = x$<br /><br />We have \\'O\\' and \\'A\\' in SOHCAH<strong>TOA</strong>, so we know we need to use the $tan$ formula:</p>\\n<p>\\\\[ tan(Angle) = \\\\frac{Opposite}{Adjacent}\\\\]</p>\\n<p>Now we subsitute the values we have in this particular question</p>\\n<p>\\\\[ tan(\\\\var{angle}) = \\\\frac{\\\\var{bc}}{x}\\\\]<br /><br />and rearrange to give:</p>\\n<p>\\\\[ x = \\\\frac{\\\\var{bc}}{tan(\\\\var{angle})} \\\\]<br /><br /><em>Make sure your calculator is set to \\'degree\\' mode, if you get an odd answer you are likely in the wrong mode!</em></p>\\n<p>\\\\[ x = \\\\var{precround(bc/tan(pi*angle/180),4)}\\\\]</p>\\n<p>Round as required:</p>\\n<p>\\\\[ x = \\\\var{precround(bc/tan(pi*angle/180),2)}\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}}, "variablesTest": {"condition": "precround(180*(arcsin(bc/(ab)))/pi,1) = precround(angle,1)", "maxRuns": "6"}, "ungrouped_variables": [], "variable_groups": [{"name": "Unnamed group", "variables": ["ab", "ac", "bc", "diagram", "angle", "SCT", "AngORside", "answer"]}, {"name": "triangle types", "variables": ["d_t_a_2", "d_t_s_1", "d_s_a_1", "d_c_a_1", "d_c_s_1", "d_s_s_1", "d_c_s_2", "d_t_a_1", "d_t_s_2", "d_s_a_2", "d_s_s_2", "d_c_a_2"]}, {"name": "advice", "variables": ["advice", "tan_a", "sin_a", "cos_a", "sin_bc", "cos_ac", "tan_ac"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", 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