cos rule - find an angle - 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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Published this.

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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 sine 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 angle {dspchosenangle}. Angle {dspchosenangle} is obtuse.

Give your answer rounded to the nearest minute.

not to scale

Give any introductory information the student needs.

			Name	Type	Generated Value

side_a_val	number	8.6
side_b_val	decimal	dec("17.9")
side_c_val	decimal	dec("18.5")
angle_A_deg	integer	27
angle_A_min	integer	14
angle_A_val	number	0.475311333
angle_B_val	number	1.2650728195
angle_C_val	number	1.4012085011
obtuse	integer	0
test	number	1.2650728195

			Name	Type	Generated Value

aA	string
aB	string	B
aC	string
sa	number	8.6
sb	decimal	dec("17.9")
sc	decimal	dec("18.5")
unitchoices	list	[ "mm", "cm", "m", "km" ]
units	string	km
dsp3rdside	integer	1
angleA	string	27°14'
angleB	string	72°29'
angleC	string	80°17'

			Name	Type	Generated Value

findvar	integer	1
helpingvar	integer	0
othervar	integer	2
answer	number	1.264983372
answer_deg	decimal	dec("72")
answer_min	decimal	dec("29")
side_vals	list	List of 3 items
side_dsp_vals	list	List of 3 items
side_dsp_names	list	[ "a", "b", "c" ]
angle_dsp_vals	list	List of 3 items
angle_dsp_names	list	[ "A", "B", "C" ]
dspchosenangle	string	B
angle_vals	list	List of 3 items

			Name	Type	Generated Value

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.

Can an exam override the value of this variable?

Generated value: `number`

8.6

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

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1. Gap degrees Number entry
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2. Gap minutes Number entry
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{dspchosenangle} = degrees °minutes'

Advice

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

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

Take the inverse cos of both sides:

$\var{dspchosenangle} = \cos^{-1}(\frac{\var{side_dsp_vals[helpingvar]}^2 +\var{side_dsp_vals[othervar]}^2 -\var{side_dsp_vals[findvar]}^2}{2 \times \var{side_dsp_vals[helpingvar]} \times \var{side_dsp_vals[othervar]}}) = \var{answer_deg}$ ° $\var{answer_min}$ '

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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.

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cos rule - find an angle

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Merryn Horrocks 4 years, 8 months ago

Merryn Horrocks 4 years, 8 months ago

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 an angle

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

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

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Generated value: `number`