MATH6058 Solve for x and y on a given triangle and calculate the area

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Catherine Palmer

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7 years, 4 months ago

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Catherine Palmer 7 years, 4 months ago

Gave some feedback: Ready to use

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Catherine Palmer 7 years, 5 months ago

Created this as a copy of Q4 Solve for x and y on a given triangle and calculate the area.

Name	Status	Author	Last Modified
Q3 Solve for x and y on a given triangle	draft	TEAME CIT	05/10/2016 14:45
Q4 Solve for x and y on a given triangle and calculate the area	draft	TEAME CIT	08/10/2016 21:39
Q1.1 Pythagoras' Theorem and naming sides of right angled triangle	draft	TEAME CIT	08/10/2016 21:38
Q3: Solve for x and y on a given triangle	draft	Denis Flynn	17/01/2017 13:15
MATH6058 Pythagoras' Theorem and naming sides of right angled triangle	draft	Catherine Palmer	23/10/2017 00:40
MATH6058 Solve for x and y on a right angled triangle	draft	Catherine Palmer	23/10/2017 00:42
MATH6058 Solve for x and y on a given triangle and calculate the area	Ready to use	Catherine Palmer	29/03/2018 11:27
Simon's copy of Q1.1 Pythagoras' Theorem and naming sides of right angled triangle	draft	Simon Thomas	01/05/2019 14:59
Simon's copy of Q1.1 Pythagoras' Theorem	draft	Simon Thomas	01/05/2019 15:44
Simon's copy of Q3 Solve for x and y on a given triangle	draft	Simon Thomas	02/05/2019 09:47
Simon's copy of Q4 Solve for x and y on a given triangle and calculate the area	draft	Simon Thomas	02/05/2019 10:42
Maria's copy of Q1.1 Pythagoras' Theorem and naming sides of right angled triangle	draft	Maria Aneiros	29/05/2019 08:42
Using Pythagoras to find a missing side (Eukleides diagrams)	Ready to use	Deirdre Casey	10/05/2023 09:12
Ann's copy of Using Pythagoras to find a missing side (Eukleides diagrams)	draft	Ann Smith	11/06/2019 10:48

There are 45 other versions that do you not have access to.

Question statement

Watch the video below to better understand the sine rule formula

Video

Solve the following mensuration questions to 2 decimal places:

Note: You may need to scroll down to see the diagrams.

Give any introductory information the student needs.

			Name	Type	Generated Value

ang31a	integer	73
lent31a	integer	88
ans31a	number	70.49
ang32a	integer	50
ans32a	number	77.18
h3a	number	59.12
ans33a	number	2601.28
l2a	number	49.61

			Name	Type	Generated Value

lent11	integer	38
ans11	number	45.28
ans12	number	51.03
lent22	integer	36
lent21	integer	77
ans21	number	19.30
ang31	integer	78
lent31	integer	105
ans31	number	79.77
ang32	integer	54
ans32	number	86.84
h3	number	64.53
ans33	number	3387.83
l2	number	46.89
ang21	integer	135
ang11	integer	75
ang12	integer	59
h1	number	32.57
w1	number	31.46
ans13	number	831.02
ans22	number	25.7
ans23	number	47.22
h2	number	25.45
w2	number	72.67
ans24a	number	924.73
ans24	number	601.01

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(71..85)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

ans31a
ans32a

Advice
"Part d)" - prompt

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part d) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

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

Find the values of x and y:

Note: Keep calculations to 3 decimal places for accuracy but the final answers must be entered to 2 decimal places.

{tri(ans12,h1,lent11,ang11,ang12,w1)}

x = Gap 0.mm

y = Gap 1.mm

Area = Gap 2. $mm^2$

Advice

i) $\frac{\var{lent11}}{\sin(180^{\circ}-(\var{ang11}^{\circ}+\var{ang12}^{\circ}))} = \frac{x}{\sin(\var{ang12}^{\circ})}$

$x = \frac{\var{lent11}}{\sin(180^{\circ}-(\var{ang11}^{\circ}+\var{ang12}^{\circ}))} \times \sin(\var{ang12}^{\circ}) = \var{ans11}mm$

$\frac{\var{lent11}}{\sin(180^{\circ}-(\var{ang11}^{\circ}+\var{ang12}^{\circ}))} = \frac{y}{Sin(\var{ang11}^{\circ})}$

$y = \frac{\var{lent11}}{Sin(180^{\circ}-(\var{ang11}^{\circ}+\var{ang12}^{\circ}))} \times \sin(\var{ang11}^{\circ}) = \var{ans12}mm$

$\frac{1}{2} \times \var{ans11} \times \var{lent11} \times \sin(\var{ang11}^{\circ}) = \var{ans13}mm^2$

ii) $\frac{\var{lent21}}{\sin(\var{ang21}^{\circ})} = \frac{\var{lent22}}{\sin(x^{\circ})}$

$\sin(x^{\circ}) = \var{lent22} \div \frac{\var{lent21}}{\sin(\var{ang21}^{\circ})}$

$x = \var{ans21}^{\circ}$

$y = 180^{\circ} - (\var{ans21}^{\circ}+\var{ang21}^{\circ}) = \var{ans22}^{\circ}$

$\frac{\var{lent21}}{\sin(\var{ang21}^{\circ})} = \frac{z}{\sin(\var{ans22}^{\circ})}$

$z = \frac{\var{lent21}}{\sin(\var{ang21})} \times \sin(\var{ans22}) = \var{ans23}mm$

$\frac{1}{2} \times \var{ans23} \times \var{lent22} \times \sin(\var{ang21}^{\circ}) = \var{ans24}mm^2$

iii) $\frac{\var{lent31}}{\sin(\var{ang31}^{\circ})} = \frac{x}{\sin(180^{\circ}-(\var{ang31}^{\circ}+\var{ang32}^{\circ}))}$

$x = \frac{\var{lent31}}{\sin(\var{ang31}^{\circ})} \times \sin(180^{\circ}-(\var{ang31}^{\circ}+\var{ang32}^{\circ})) = \var{ans31}mm$

$\frac{\var{lent31}}{\sin(\var{ang31}^{\circ})} = \frac{y}{\sin(\var{ang32}^{\circ})}$

$y = \frac{\var{lent31}}{\sin(\var{ang31}^{\circ})} \times \sin(\var{ang32}^{\circ}) = \var{ans32}mm$

$\frac{1}{2} \times \var{ans31} \times \var{ans32} \times \sin(\var{ang31}^{\circ}) = \var{ans33}mm^2$

iv) $\frac{\var{lent31a}}{\sin(\var{ang31a}^{\circ})} = \frac{x}{\sin(\var{ang32a}^{\circ})}$

$x = \frac{\var{lent31a}}{\sin(\var{ang31a}^{\circ})} \times \sin(\var{ang32a}^{\circ}) = \var{ans31a}mm$

$\frac{\var{lent31a}}{\sin(\var{ang31a}^{\circ})} = \frac{y}{\sin(180^{\circ}-(\var{ang32a}^{\circ}+\var{ang31a}^{\circ}))}$

$y = \frac{\var{lent31a}}{\sin(\var{ang31a})} \times \sin(180-(\var{ang32a}+\var{ang31a})) = \var{ans32a}mm$

$\frac{1}{2} \times \var{ans31a} \times \var{ans32a} \times \sin(\var{ang31a}^{\circ}) = \var{ans33a}mm^2$

Give a worked solution to the whole question.

URL

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Part	Test	Passed?
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Information only
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This question is used in the following exams:

test1 by Garrett Keane in Garrett's workspace.
Week 8 Quiz by Gavin Mountjoy in Gavin's workspace.
Gavin's copy of Week 8 Quizb by Gavin Mountjoy in Gavin's workspace.
MATH6058 Tutorial 3 by Catherine Palmer in MATH6058 Engineering Maths 1.
Marco's copy of MATH6058 Tutorial 3 by Marco Vitturi in Marco's workspace.

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MATH6058 Solve for x and y on a given triangle and calculate the area

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Catherine Palmer 7 years, 4 months ago

Catherine Palmer 7 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Error

MATH6058 Solve for x and y on a given triangle and calculate the area

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Catherine Palmer 7 years, 4 months ago

Catherine Palmer 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`