Ben's copy of 3 point triangle

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Ben Brawn

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Ben Brawn 7 years, 11 months ago

Created this as a copy of 3 point triangle.

Name	Status	Author	Last Modified
3 point triangle TestBed	draft	David Wishart	02/05/2017 22:00
3 point triangle	draft	David Wishart	31/03/2025 15:39
Ben's copy of 3 point triangle	draft	Ben Brawn	02/05/2017 05:21
3 side triangle	draft	David Wishart	07/05/2017 23:04
Right Angle triangle	draft	David Wishart	10/06/2017 22:53
Trigonometry Q2 Right angled triangle	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q3 Right angled triangle	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q4 Sine rule	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q5 Cosine rule	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry to Find Missing Length	draft	Gareth Woods	21/07/2017 16:00
Trigonometry to Find Angle	draft	Gareth Woods	21/07/2017 16:02
Paul's copy of Trigonometry Q4 Sine rule	draft	Paul Hancock	05/09/2017 03:32
Question 4	draft	Paul Hancock	07/09/2017 01:42
Question 5	draft	Paul Hancock	05/09/2017 03:40
Right Triangle	draft	Paul Hancock	05/09/2017 03:57
MATH6058 Trigonometry Cosine rule	draft	Catherine Palmer	24/10/2017 11:06
Trigonometry Q1	Ready to use	David Wishart	05/06/2023 13:11
Kwame's copy of Paul's copy of Trigonometry Q4 Sine rule	draft	Kwame D Dwamena	15/03/2018 15:37
Kwame's copy of MATH6058 Trigonometry Cosine rule	draft	Kwame D Dwamena	15/03/2018 15:39
Trigonometry Application	draft	Mark Hodds	16/03/2018 09:35
Trigonometry Cosine rule	draft	Mark Hodds	16/03/2018 09:48
Trigonometry Sine rule	draft	Mark Hodds	16/03/2018 09:38
Trigonometry Sine rule	draft	Mark Hodds	16/03/2018 09:46
Christian's copy of Trigonometry Q1	draft	Christian Lawson-Perfect	13/06/2018 09:03
Network Demo	draft	Paul Hancock	04/07/2018 01:32
Sine, cosine, and area rules	draft	Sean Gardiner	17/02/2019 20:47
Sine, cosine, and area rules	draft	Sean Gardiner	13/02/2019 00:37
Right-triangle trigonometry	draft	Sean Gardiner	16/12/2018 21:58
Right-triangle trigonometry [OLD]	draft	Sean Gardiner	21/12/2021 03:15
Trigonometry Q3 (Right angled triangle)	draft	Michael Proudman	07/12/2021 10:48
Trigonometry to Find Missing Length (Right Angled Triangle)	draft	Michael Proudman	07/12/2021 10:48
Michael's copy of Trigonometry Q1	draft	Michael Proudman	07/12/2021 10:48
Michael's copy of Right-triangle trigonometry	draft	Michael Proudman	07/12/2021 10:48
Sine, cosine, and area rules (radians)	draft	Sean Gardiner	17/02/2019 20:47
SOHCAHTOA applied problem	Should not be used	Ruth Hand	12/07/2022 15:05
Simon's copy of Sine, cosine, and area rules	draft	Simon Thomas	02/05/2019 10:45
Simon's copy of Trigonometry Cosine rule	draft	Simon Thomas	02/05/2019 10:59
Meetu's copy of Michael's copy of Trigonometry Q1	draft	Meetu Chhabra	21/05/2019 05:14
Trigonometry Q1	draft	Meetu Chhabra	21/05/2019 05:15
Maria's copy of Sine, cosine, and area rules	draft	Maria Aneiros	24/05/2019 00:52
Maria's copy of Meetu's copy of Michael's copy of Trigonometry Q1	draft	Maria Aneiros	29/05/2019 08:19
Maria's copy of Trigonometry Q1	draft	Maria Aneiros	29/05/2019 07:52
Trigonometry: Sine Rule	draft	Xiaodan Leng	10/07/2019 22:55
Trigonometry Cosine rule	draft	Xiaodan Leng	10/07/2019 22:55
Right-triangle trigonometry	draft	Sean Gardiner	17/09/2020 23:54
Sine, cosine, and area rules	draft	Sean Gardiner	09/02/2020 22:14
Michael's copy of Right-triangle trigonometry	draft	Michael Proudman	07/12/2021 10:48
Pythagoras: calculating side length	Ready to use	Ruth Hand	08/03/2023 14:52
Right angled triangles: SOHCAHTOA 3 - random side or angle	Ready to use	Ruth Hand	27/09/2022 09:01
Right angled triangles: SOHCAHTOA 1 - find angle	Ready to use	Ruth Hand	27/09/2022 09:01
Right angled triangles: SOHCAHTOA 2 - find side	Ready to use	Ruth Hand	27/09/2022 09:01
GB1 Trigonometry - missing side	Ready to use	Megan Oliver	14/02/2025 14:31
GB6 Trigonometry - non-right angled trig	Ready to use	Oliver Spenceley	09/04/2024 17:51
GB2 Trigonometry - missing angle	Ready to use	Will Morgan	14/02/2025 14:29
GA2 Pythagoras - triangle	Ready to use	Will Morgan	09/04/2024 17:45

There are 172 other versions that do you not have access to.

Question statement

Referring to the line below.

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

x1	integer	11
x2	integer	38
y1	integer	29
y2	integer	9
unitList	list	[ "mm", "cm", "m", "km" ]
units	integer	1
c		Definition of variable `c` is empty.
m		Definition of variable `m` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5..20)

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Description

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Generated value: `integer`

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{plotgraph(x1,x2,y1,y2,units)}

All units are in mmcmmkm

Advice

(i) To find $f(\var{x1})$ , you start at $\var{x1}$ on the $x$ -axis, go up or down until you reach the blue line, and then look at the $y$ -coordinate. This $y$ -coordinate is the answer. In this question, after going up/down from $\var{x1}$ , we reach the $y$ -coordinate $\var{y1}$ , so the answer is $f(\var{x1})=\var{y1}$ .

(ii) There are two options. The first option (which is not efficient) is trial-and-error: pick some random value of $x$ and determine $f(x)$ . If $f(x) = \var{y2}$ , then your pick is the answer. If not, then try a different value of $x$ , hopefully getting closer and closer each time. The second (and better) option is to 'work backwards' - we know what $f(x)$ should be, which means we know what the $y$ -coordinate should be. So start at $\var{y2}$ on the $y$ -axis, go left or right until you reach the blue line, and look at the $x$ -coordinate. In this question, after going left/right from $\var{y2}$ , we reach the $x$ -coordinate $\var{x2}$ , so this is the answer. You can check this is correct: what is $f(\var{x2})$ ? It is $\var{y2}$ , as we wanted!

(iii) The $y$ -intercept is the height at which the blue line touches the $y$ -axis. In this question, the blue line crosses the $y$ -axis at a height of $\var{c}$ , so the answer is $\var{c}$ .

(iv) To calculate the gradient, you choose two points which lie on the line, and calculate the change in height divided by the change in $x$ . It does not matter which two points you choose, but to make it easier, you should pick points whose coordinates are easy to read. In this question, two points which are on the line are $(\var{x1}, \var{y1})$ and $(\var{x2},\var{y2})$ . Then the change of height is $\var{y2} - \var{y1}$ and the change in $x$ is $\var{x2} - \var{x1}$ . Dividing gives the answer $\var{m}$ , which is the number we want.

(v) The equation of a line can be written as $y = mx + c$ . $m$ is the gradient and $c$ is the $y$ -intercept. But we have calculated these two quantities in the previous two questions: the $y$ -intercept was $\var{c}$ and the gradient was $\var{m}$ . Replacing $m$ and $c$ with these numbers gives the equation $y= \var{m}x + \var{c}$ , which is the answer.

(vi) This question is asking exactly the same thing as the question in (ii), but is phrased differently. This is because the definition of $f^{-1}$ is that it is the function which un-does what $f$ does. For example, we know that $f(\var{x1})=\var{y1}$ - therefore, automatically, $f^{-1}(\var{y1})$ has to be $\var{x1}$ . Re-worded, $f$ maps $\var{x1}$ to $\var{y1}$ , so because $f^{-1}$ un-does this, it means $f^{-1}$ maps $\var{y1}$ back to $\var{x1}$ . Back to the question at hand, it asked what $f^{-1}(\var{y2})$ is. By definition, this means we want to know what value of $x$ is needed to get $f(x) = \var{y2}$ , which is exactly what was asked in (ii).

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Taxonomy: mathcentre

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Ben Brawn 7 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

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Ben's copy of 3 point triangle

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ben Brawn 7 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`