Right angled triangle finding side Pythagoras - Topic 1.3 JSXGraph version

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Merryn Horrocks

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Ready to use

2 years, 4 months ago

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Don Shearman 2 weeks, 4 days ago

Published this.

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Merryn Horrocks 2 years, 4 months ago

Gave some feedback: Ready to use

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Merryn Horrocks 2 years, 4 months ago

Created this as a copy of Baseline Trigonometry 1 adjacent JSXGraph version.

Name	Status	Author	Last Modified
Baseline Trigonometry 1 adjacent JSXGraph version	Ready to use	Jim Pettigrew	11/12/2023 01:47
Right angled triangle finding side Pythagoras - Topic 1.3 JSXGraph version	Ready to use	Merryn Horrocks	10/04/2025 05:22

There are 31 other versions that do you not have access to.

Question statement

Refer to the triangle below.

Give any introductory information the student needs.

			Name	Type	Generated Value

diagram

jsxgraphboard

HTML node

			Name	Type	Generated Value

ab	integer	-2
bc	integer	-2
hypotenuse	integer	3
ans_squared	number	5
answer	number	2.24

			Name	Type	Generated Value

left	number	-2.6
right	number	0.6
top	number	0.6
bottom	number	-2.6
boxHeight	number	3.2
boxwidth	number	3.2
axesV	number	500

			Name	Type	Generated Value

XCoordOfRA	number	-1.8
YCoordOfRA	number	-0.2
horizontalSideMidpointX	rational	-1
horizontalSideMidpointY	integer	0
verticalSideMidpointX	number	-2.25
verticalSideMidpointY	rational	-1
hypotenuseMidpointX	rational	-1
hypotenuseMidpointY	decimal	dec("-1.1")
horizontalLabelPosition	integer	20
verticalLabelPosition	integer	-25
hypotenuseLabelPositionX	integer	15
hypotenuseLabelPositionY	integer	-15
horizontalAngleHorizontalPoint	list	[ -1, 0 ]
horizontalAngleVerticalPoint	list	[ 0.7071067812, 0.7071067812 ]

			Name	Type	Generated Value

abPortionPre	number	0.2
bcPortionPre	number	0.2
vertexInc	number	0.6
alpha	number	-2.3561944902
adjRatioW	number	1
adjRatioH	number	1

			Name	Type	Generated Value

aLabel	string	'3 km'
bLabel	string	'2 km'
cLabel	string	'2 km'

			Name	Type	Generated Value

			unitList	list	[ "mm", "cm", "m", "km" ]
			units	string	km

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
jessiecode(500,{axesV},[{left},{top},{right},{bottom}],
"aLabel={aLabel};bLabel={bLabel};cLabel={cLabel};ab={ab};bc={bc};XCoordOfRA={XCoordOfRA};YCoordOfRA={YCoordOfRA};hSMPX={horizontalSideMidpointX};hSMPY={horizontalSideMidpointY};vSMPX={verticalSideMidpointX};vSMPY={verticalSideMidpointY};hypMPX={hypotenuseMidpointX};hypMPY={hypotenuseMidpointY};hAHP0={horizontalAngleHorizontalPoint[0]};hAHP1={horizontalAngleHorizontalPoint[1]};hAVP0={horizontalAngleVerticalPoint[0]};hAVP1={horizontalAngleVerticalPoint[1]};horizontalLabelPosition={horizontalLabelPosition};verticalLabelPosition={verticalLabelPosition};hypotenuseLabelPositionX={hypotenuseLabelPositionX};hypotenuseLabelPositionY={hypotenuseLabelPositionY};"+safe(""" // [l,t,r,b]
​
// mark the points of the triangle    
  point(0,0) <<id:'A', fixed: true, snapToGrid: false, withLabel: true, label: <<offset: [0,horizontalLabelPosition], fontSize: 20>>, showInfobox: false, size: 0>>;
  point(ab,0) <<id:'B', fixed: true, snapToGrid: false, withLabel: true, label: <<offset: [0,horizontalLabelPosition], fontSize: 20>>, showInfobox: false, size: 0>>;
  point(ab,bc) <<id:'C', fixed: true, snapToGrid: false, withLabel: true, label: <<offset: [verticalLabelPosition,horizontalLabelPosition], fontSize: 20>>, showInfobox: false, size: 0>>;
​
// Draw triangle    
  segment(A,B) <<id: 's1', fixed: true, highlight: false, useMathjax: true, withLabel: false>>;
  segment(B,C) <<id: 's2', fixed: true, highlight: false, useMathjax: true, withLabel: false>>;
  segment(C,A) <<id: 's3', fixed: true, highlight: false, useMathjax: true, withLabel: false>>;
  
// Mark in the right angle marker    
  point(XCoordOfRA,0) <<id:'rac1', snapToGrid: false, withLabel: false, showInfobox: false, size: 0>>;
  point(XCoordOfRA,YCoordOfRA) <<id:'rac2', snapToGrid: false, withLabel: false, showInfobox: false, size: 0>>;
  point(ab,YCoordOfRA) <<id:'rac3', snapToGrid: false, withLabel: false, showInfobox: false, size: 0>>;
​
// Add the side labels.    
  point(hSMPX,hSMPY) <<id:'pfl1', fixed: true, name: 'c', withLabel: false, label: <<offset: [0,horizontalLabelPosition], fontSize: 20>>, showInfobox: false, size: 0>>;
  point(vSMPX,vSMPY) <<id:'pfl2', fixed: true, name: bLabel, withLabel: true, label: <<offset: [verticalLabelPosition,0], fontSize: 20>>, showInfobox: false, size: 0>>;
  point(hypMPX,hypMPY) <<id:'pfl3', fixed: true, name: aLabel, withLabel: true, label: <<offset: [hypotenuseLabelPositionX,hypotenuseLabelPositionY], fontSize: 20>>, showInfobox: false, size: 0>>; 
​
// Set up the angle marker    
  point(hAHP0,hAHP1) <<id: 'hAHP', fixed: true, withLabel: false, showInfobox: false, size: 0>>;
  point(hAVP0,hAVP1) <<id: 'hAVP', fixed: true, withLabel: false, showInfobox: false, size: 0>>;
  point(hAHP0,hAVP1) <<id: 'bCP1', fixed: true, withLabel: false, showInfobox: false, size: 0>>;
  point(hAHP0,hAVP1) <<id: 'bCP2', fixed: true, withLabel: false, showInfobox: false, size: 0>>;
  
// Add the angle markers    
hAngle = function() {if (ab>0) {
    if (bc>0) {
      return angle(B,A,C) <<name:'x', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [10,0], fontSize: 20, color: 'black'>>>>;
    } else {
      return angle(C,A,B) <<name:'x', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [10,-10], fontSize: 20, color: 'black'>>>>;
    }
  } else {
    if (bc>0) {
      return angle(C,A,B) <<name:'x', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [-10,0], fontSize: 20, color: 'black'>>>>;
    } else {
      return angle(B,A,C) <<name:'x', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [-10,0], fontSize: 20, color: 'black'>>>>;
    }
  }
};
rAngle = function() {if (ab>0) {
    if (bc>0) {
      return angle(C,B,A) <<name:'x', type:'sector', orthoType:'square', withLabel: false, color: '#0072b2', fillOpacity: 0, radius: ab/10>>;
    } else {
      return angle(A,B,C) <<name:'x', type:'sector', orthoType:'square', withLabel: false, color: '#0072b2', fillOpacity: 0, radius: ab/10>>;
    }
  } else {
    if (bc>0) {
      return angle(A,B,C) <<name:'x', type:'sector', orthoType:'square', withLabel: false, color: '#0072b2', fillOpacity: 0, radius: -ab/10>>;
    } else {
      return angle(C,B,A) <<name:'x', type:'sector', orthoType:'square', withLabel: false, color: '#0072b2', fillOpacity: 0, radius: -ab/10>>;
    }
  }
};
vAngle = function() {if (ab>0) {
    if (bc>0) {
      return angle(A,C,B) <<name:'y', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [0,-12], fontSize: 20, color: 'black'>>>>;
    } else {
      return angle(B,C,A) <<name:'y', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [0,12], fontSize: 20, color: 'black'>>>>;
    }
  } else {
    if (bc>0) {
      return angle(B,C,A) <<name:'y', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [0,0], fontSize: 20, color: 'black'>>>>;
    } else {
      return angle(A,C,B) <<name:'y', type:'sector', orthoType:'square', withLabel: true, label: <<offset: [0,12], fontSize: 20, color: 'black'>>>>;
    }
  }
};    
​
  //hAngle();
  rAngle();
  //vAngle();
    
"""),
[
    "axis": false,
    "keepaspectratio": true
    ])

JME function reference

This variable is an interactive HTML node. Interactive HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

Description

Draw the right angled triangle

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `jsxgraphboard`

0,0

2 km

3 km

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

{diagram}

What is the length of side $AB$ ?

Please give answer to 2 decimal places

$AB =$ Unnamed gap {units}

Advice

By Pythagoras' Theorem:

$\begin{align}\var{abs(bc)}^2+c^2&=\var{hypotenuse}^2\\c^2&=\var{hypotenuse}^2-\var{abs(bc)}^2\\&=\var{hypotenuse^2-bc^2}\\c&=\sqrt{\var{hypotenuse^2-bc^2}}\end{align}$

$\therefore \var{simplify(expression("c=\sqrt("+hypotenuse+"*"+hypotenuse+"-"+bc+"*"+bc+ ")"),"all")}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Right angled triangle finding side Pythagoras - Topic 1.3 JSXGraph version

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 2 weeks, 4 days ago

Merryn Horrocks 2 years, 4 months ago

Merryn Horrocks 2 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `jsxgraphboard`

Parts

Gap-fill

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Error

Right angled triangle finding side Pythagoras - Topic 1.3 JSXGraph version

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 2 weeks, 4 days ago

Merryn Horrocks 2 years, 4 months ago

Merryn Horrocks 2 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: jsxgraphboard

Parts

Gap-fill

Generated value: `jsxgraphboard`