Trigonometry: Cosine Rule 1

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Ben McGovern

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3 years, 7 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

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Ben McGovern 3 years, 7 months ago

Gave some feedback: Ready to use

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Ben McGovern 4 years, 6 months ago

Created this as a copy of Trigonometry: Sine Rule 2.

Name	Status	Author	Last Modified
Trigonometry: Sine Rule 1	Ready to use	Ben McGovern	09/03/2023 09:50
Trigonometry: Sine Rule 2	Ready to use	Ben McGovern	10/10/2022 13:16
Trigonometry: Cosine Rule 1	Ready to use	Ben McGovern	09/03/2023 10:26

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Question statement

Find the length of $c$ :

{geogebra_applet('https://www.geogebra.org/m/pnfanbze',defs)}

Give any introductory information the student needs.

			Name	Type	Generated Value

defs	list	[ [ "C", vector(9,6.9) ] ]
A	vector	vector(0,0)
B	vector	vector(7.2,0.0)
C	vector	vector(9,6.9)
sidea	number	7.2
sideb	number	7.13
anglec	number	104.6208739886
vec	vector	vector(1.8,6.9)
anglecr	number	104.62
sidec	number	11.3398432785
sidecr	number	11.34

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[
  ['C',C]
]

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Description

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

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Generated value: `list`

[ [ "C", vector(9,6.9) ] ]

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Parts

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1. Gap Mathematical expression
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Gap-fill

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$c=$Unnamed gap

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Advice

Since we know two side-lengths and the angle between them, we can use the cosine rule to find the third length, $c$. The cosine rules states:

\[ c^2=a^2+b^2-2ab\cos(C) \]

where $a$, $b$, and $c$ are the side-lengths, and $C$ is the angle between $a$ and $b$:

{geogebra_applet('https://www.geogebra.org/m/pg7d3hvz')}

So, for the triangle

{geogebra_applet('https://www.geogebra.org/m/pnfanbze',defs)}

we know that side $a=\var{sidea}$, side $b=\var{sideb}$, and angle $C=\var{anglecr}^\circ$. Substituting these values into the cosine rule we can calculate the length of $c$:

\[ \begin{split} c^2 &\,= \var{sidea}^2+\var{sideb}^2-2 \times \var{sidea}\times\var{sideb} \times \cos(\var{anglecr}) \\ &\,=\var{sidecr^2} \\ \implies c &\,=\var{sidecr} \text{ (2 d.p.)}. \end{split} \]

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Taxonomy: mathcentre

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 7 months ago

Ben McGovern 4 years, 6 months ago

Error in variable testing condition

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Generated value: `list`

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Trigonometry: Cosine Rule 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 7 months ago

Ben McGovern 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`