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

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4 years, 8 months ago

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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

Find the value of side {dspchosenside}. Round your answer to 1 decimal place.

not to scale

Give any introductory information the student needs.

			Name	Type	Generated Value

side_a_val	number	12.5
side_b_val	decimal	dec("11.6")
side_c_val	decimal	dec("21.5")
angle_A_deg	integer	28
angle_A_min	integer	10
angle_A_val	number	0.4916010726
angle_B_val	number	0.4502151737
angle_C_val	number	2.1997764073
obtuse	integer	1

			Name	Type	Generated Value

aA	string	28°10'
aB	string	25°48'
aC	string
sa	string	12.5 mm
sb	string	b
sc	string
unitchoices	list	[ "mm", "cm", "m", "km" ]
units	string	mm
dsp3rdangle	integer	1

			Name	Type	Generated Value

findvar	integer	1
helpingvar	integer	0
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" ]
dspchosenside	string	b
answer	number	11.5

			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.

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Generated value: `number`

12.5

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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{dspchosenside} = Unnamed gap {units}

Advice

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

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

Since the angle opposite {dspchosenside} is not given, we need to work it out, using the fact that the angles in the triangle sum to 180º.

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

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

Next we multiply both sides by ${\sin(\var{angle_dsp_vals[findvar]})}$

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

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sine 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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Error

sine 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`