Apply the cosine rule

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Anna Cartlidge

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Needs to be tested

3 years ago

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Anna Cartlidge 3 years ago

Gave some feedback: Needs to be tested

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Name	Status	Author	Last Modified
Apply the cosine rule	Needs to be tested	Newcastle University Mathematics and Statistics	12/05/2022 15:16
Clare's copy of Apply the cosine rule	draft	Clare Lundon	05/10/2016 22:55
cormac's copy of Apply the cosine rule	draft	cormac breen	05/11/2018 13:46
cormac's copy of cormac's copy of Apply the cosine rule	draft	cormac breen	05/11/2018 13:48
Apply the cosine rule (2 sides, 1 angle, degrees)	Ready to use	Andrew Chuter	06/04/2020 12:15
Area of a triangle (2 sides, 1 angle, degrees)	Ready to use	Andrew Chuter	09/04/2020 05:35

There are 24 other versions that do you not have access to.

Question statement

Suppose that $\Delta ABC$ is a triangle with all interior angles $< \dfrac{\pi}{2}$ (in other words, an acute triangle). Here all angles are expressed in radians. Suppose also that standard naming conventions are used as indicated in the picture below (not necessarily an accurate picture of $\Delta ABC$ ).

Given the following two sides and an angle, determine the third side length. Write down the side length as a whole number.

Give any introductory information the student needs.

			Name	Type	Generated Value

c4	integer	8
s3	number	0.6977129562
cc0	number	1.4122
temp2	number	0.0003575755
temp1	number	20.9996424245
b0	integer	21
cc3	number	1.4184
b3	integer	14
u2	number	0.9874183352
q0	number	0.6032388664
q3	number	0.5808823529
c0	integer	26
cc5	number	1.418
s2	number	0.7215233937
s0	number	0.7215926291
cc1	number	1.4122926536
u0	number	0.9874499414
u3	number	0.9884101367
cc2	number	1.412
aa5	number	0.772
aa4	number	0.7721926536
aa1	number	0.8061926536
aa0	number	0.8061
aa3	number	0.7722
aa2	number	0.806
x2	number	802
c31	integer	8
c32	integer	1
a0	integer	19
a3	integer	12
bb0	number	0.9232
s5	number	0.6975696667
c3	integer	17
c2	integer	28
c1	integer	9
x1	number	80
c02	integer	1
x4	number	52
x5	number	340
p3	number	0.7163865546
p0	number	0.6923076923
r0	number	0.1578947368
r3	number	0.1517857143
bb3	number	0.9510
t5	number	0.8139967811
t2	number	0.7974154976
t3	number	0.8139967811
t0	number	0.7975361678
u5	number	0.9883493348
c5	integer	18
cc4	number	1.4183926536
c01	integer	9
bb5	number	0.951
bb4	number	0.9509926536
check2	number	-0.0000073464
bb2	number	0.923
bb1	number	0.9232926536
check1	number	0.0000926536

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
max(c31,c32)

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: `integer`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$A=\var{AA0}$ , $b=\var{b0}$ , $c=\var{c0}$

Side length $a=$ Unnamed gap

Advice

a) Use the Cosine Rule to find $a$ : $a^2=b^2+c^2-2bc \cos A$ .

$a^2=\var{b0}^2+\var{c0}^2-2 \times \var{b0}\times\var{c0} \times \cos (\var{aa0})=\var{b0^2}+\var{c0^2}-\var{2*b0*c0} \times \var{cos (aa0)}$

$=\var{b0^2+c0^2-2*b0*c0* cos (aa0)}.$

Hence $a=\sqrt{\var{b0^2+c0^2-2*b0*c0* cos (aa0)}}=\var{sqrt(b0^2+c0^2-2*b0*c0* cos (aa0))}$ . To the nearest integer, this is $\var{a0}$ .

b) Use the Cosine Rule to find $b$ : $b^2=a^2+c^2-2ac \cos B$ .

$b^2=\var{a3}^2+\var{c3}^2-2 \times \var{a3}\times\var{c3} \times \cos (\var{bb3})=\var{a3^2}+\var{c3^2}-\var{2*a3*c3} \times \var{cos (bb3)}$

$=\var{a3^2+c3^2-2*a3*c3* cos (bb3)}.$

Hence $b=\sqrt{\var{a3^2+c3^2-2*a3*c3* cos (bb3)}}=\var{sqrt(a3^2+c3^2-2*a3*c3* cos (bb3))}$ . To the nearest integer, this is $\var{b3}$ .

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Anna Cartlidge 3 years ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Apply the cosine rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Anna Cartlidge 3 years ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`