Q4 Solve for x and y on a given triangle and calculate the area

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TEAME CIT

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TEAME CIT 8 years, 5 months ago

Published this.

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TEAME CIT 9 years, 1 month ago

Created this as a copy of Q3 Solve for x and y on a given triangle.

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	80
lent31a	integer	74
ans31a	number	60.01
ang32a	integer	53
ans32a	number	54.96
h3a	number	43.89
ans33a	number	1623.93
l2a	number	33.08

			Name	Type	Generated Value

lent11	integer	35
ans11	number	39.96
ans12	number	42.65
lent22	integer	47
lent21	integer	81
ans21	number	30.17
ang31	integer	78
lent31	integer	108
ans31	number	85.81
ang32	integer	51
ans32	number	85.81
h3	number	66.69
ans33	number	3601.26
l2	number	54.00
ang21	integer	120
ang11	integer	69
ang12	integer	61
h1	number	30.61
w1	number	25.68
ans13	number	652.76
ans22	number	29.83
ans23	number	46.52
h2	number	40.71
w2	number	70.03
ans24a	number	1425.46
ans24	number	946.76

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 answers to 3 decimal places for accuracy.

{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.

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

Math6000 Trigonometry by TEAME CIT in MATH6000 Essential Mathematical Skills.
Math6000 (WS5-8) by Julie Crowley in MATH6000 Essential Mathematical Skills.
Trigonometry by Deirdre Casey in Deirdre's workspace.
Apprentices Year 1 Trigonometry by Aoife O'Brien in Aoife's workspace.
claire's copy of Trigonometry by claire lines in claire's workspace.

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Q4 Solve for x and y on a given triangle and calculate the area

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

TEAME CIT 8 years, 5 months ago

TEAME CIT 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Q4 Solve for x and y on a given triangle and calculate the area

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

TEAME CIT 8 years, 5 months ago

TEAME CIT 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`