sine 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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Merryn Horrocks 4 years, 8 months ago

Gave some feedback: Ready to use

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Merryn Horrocks 4 years, 8 months ago

Created this as a copy of sine rule - find a side.

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 sine 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	12.1
side_b_val	decimal	dec("18.5")
side_c_val	decimal	dec("23.7")
angle_A_deg	integer	30
angle_A_min	integer	12
angle_A_val	number	0.5270894341
angle_B_val	number	0.8790641666
angle_C_val	number	1.7354390529
obtuse	integer	1
test	boolean	false

			Name	Type	Generated Value

aA	string	A
aB	string	50°22'
aC	string
sa	string	12.1 cm
sb	string	18.5 cm
sc	string
unitchoices	list	[ "mm", "cm", "m", "km" ]
units	string	cm
dsp3rdside	integer	0

			Name	Type	Generated Value

findvar	integer	0
helpingvar	integer	1
othervar	integer	2
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" ]
answer_acute	decimal	dec("5.278934522696033799143377496240190126127e-1")
dspchosenangle	string	A
answer_deg	decimal	dec("30")
answer_min	decimal	dec("15")
answer	decimal	dec("5.278934522696033799143377496240190126127e-1")
test	boolean	false

			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`

12.1

← Depends on:

angle_A_val
side_b_val
side_c_val

→ Used by:

angle_B_val
side_dsp_vals
side_vals

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap degrees Number entry
  Add
2. Gap minutes Number entry
  Add

Gap-fill

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{dspchosenangle} = degrees °minutes'

Advice

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

This means that we need to find the value of the side opposite angle{dspchosenangle} and one other side and opposite angle.

$\frac{\var{side_dsp_vals[findvar]}}{\sin(\var{dspchosenangle})}=\frac{\var{side_dsp_vals[helpingvar]}}{\sin(\var{angle_dsp_vals[helpingvar]})}$

Next we multiply both sides by ${\sin(\var{dspchosenangle})}$ :

$\var{side_dsp_vals[findvar]}=\frac{\sin(\var{dspchosenangle})\times \var{side_dsp_vals[helpingvar]}}{\sin(\var{angle_dsp_vals[helpingvar]})}$

Multiply both sides by $\sin(\var{angle_dsp_vals[helpingvar]})$ :

$\var{side_dsp_vals[findvar]}\times \sin(\var{angle_dsp_vals[helpingvar]}) =\sin(\var{dspchosenangle})\times \var{side_dsp_vals[helpingvar]}$

Divide both sides by $\var{side_dsp_vals[helpingvar]}$ :

$\frac{\var{side_dsp_vals[findvar]}\times\sin(\var{angle_dsp_vals[helpingvar]})}{\var{side_dsp_vals[helpingvar]}} =\sin(\var{dspchosenangle})$

Swap the sides around and take the inverse sin of both sides:

$\sin(\var{dspchosenangle})=\frac{\var{side_dsp_vals[findvar]}\times\sin(\var{angle_dsp_vals[helpingvar]})}{\var{side_dsp_vals[helpingvar]}}$

$\var{dspchosenangle} = sin^{-1}(\frac{\var{side_dsp_vals[findvar]}\times\sin(\var{angle_dsp_vals[helpingvar]})}{\var{side_dsp_vals[helpingvar]}}) = \var{answer_deg}$ ° $\var{answer_min}$ '

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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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sine rule - find an angle

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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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sine 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

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`