cos rule - find a side - Numbas at mathcentre.ac.uk

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Merryn Horrocks

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Merryn Horrocks

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4 years, 8 months ago

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Merryn Horrocks 4 years, 8 months ago

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Merryn Horrocks 4 years, 8 months ago

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Merryn Horrocks 4 years, 8 months ago

Created this as a copy of cos rule - find an angle.

Name	Status	Author	Last Modified
sine rule - find a side	Ready to use	Merryn Horrocks	03/01/2023 06:04
sine rule - find an angle	Ready to use	Merryn Horrocks	03/01/2023 06:04
cos rule - find an angle	Ready to use	Merryn Horrocks	03/01/2023 06:04
cos rule - find a side	Ready to use	Merryn Horrocks	03/01/2023 06:04

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Question statement

Use the cosine rule to find the value of {dspchosenside}. Give your answer rounded to the 1 decimal place.

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Give any introductory information the student needs.

			Name	Type	Generated Value

side_a_val	number	7.5
side_b_val	decimal	dec("5.4")
side_c_val	decimal	dec("10.7")
angle_A_deg	integer	40
angle_A_min	integer	21
angle_A_val	number	0.7042403532
angle_B_val	number	0.4904375198
angle_C_val	number	1.9469147806
obtuse	integer	1
test	number	0.4904375198

			Name	Type	Generated Value

aA	string	40°21'
aB	string	28°6'
aC	string
sa	number	7.5
sb	decimal	dec("5.4")
sc	string	c
unitchoices	list	[ "mm", "cm", "m", "km" ]
units	string	m
dsp1angle	integer	0

			Name	Type	Generated Value

findvar	integer	2
helpingvar	integer	0
othervar	integer	1
answer	number	10.7
side_vals	list	List of 3 items
side_dsp_vals	list	List of 3 items
side_dsp_names	list	[ "a", "b", "c" ]
angle_vals	list	List of 3 items
angle_dsp_vals	list	List of 3 items
angle_dsp_names	list	[ "A", "B", "C" ]
dspchosenside	string	c

			Name	Type	Generated Value

dspchosenangle

Definition of variable dspchosenangle is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(cosrule_side(side_b_val,side_c_val,angle_A_val),1)

JME function reference

Description

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

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Generated value: `number`

7.5

← Depends on:

This variable doesn't seem to be used anywhere.

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1. Gap length Number entry
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{dspchosenangle} = length {units}

Advice

To find the value of {dspchosenside} we need to use the cosine rule.

We need to use the angle opposite {dspchosenside} but this is not given so we need to work it out:

angle = 180° - {angle_dsp_vals[helpingvar]} - {angle_dsp_vals[othervar]} = {angle_dsp_vals[findvar]}

$\var{dspchosenside}^2 = \var{side_dsp_vals[helpingvar]}^2 + \var{side_dsp_vals[othervar]}^2 - 2 \times \var{side_dsp_vals[helpingvar]} \times \var{side_dsp_vals[othervar]} \times \cos(\var{angle_dsp_vals[findvar]})$

Take the square root of both sides:

$\var{dspchosenside} = \sqrt{\var{side_dsp_vals[helpingvar]}^2 + \var{side_dsp_vals[othervar]}^2 - 2 \times \var{side_dsp_vals[helpingvar]} \times \var{side_dsp_vals[othervar]} \times \cos(\var{angle_dsp_vals[findvar]})}=\var{side_dsp_vals[findvar]}$ {units}

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This question is used in the following exams:

s2-trig by Merryn Horrocks in Standard Maths.
Harry's copy of s2-trig by Harry Flynn in First year maths.
trig + geometry by abc temp in abc's workspace.
Maths progress by David Doyle in David's workspace.

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cos rule - find a side

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Taxonomy: mathcentre

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Checkpoint description

Merryn Horrocks 4 years, 8 months ago

Merryn Horrocks 4 years, 8 months ago

Merryn Horrocks 4 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

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cos rule - find a side

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 4 years, 8 months ago

Merryn Horrocks 4 years, 8 months ago

Merryn Horrocks 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`