Apply the cosine rule

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Anna Cartlidge

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Needs to be tested

2 years, 10 months ago

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Anna Cartlidge 2 years, 10 months ago

Gave some feedback: Needs to be tested

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

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	16
s3	number	0.8968517769
cc0	number	1.5208
temp2	number	0.0001020048
temp1	number	24.9998979952
b0	integer	25
cc3	number	1.4066
b3	integer	13
u2	number	0.9987604191
q0	number	0.5086206897
q3	number	0.8125
c0	integer	29
cc5	number	1.407
s2	number	0.5513653943
s0	number	0.5510316446
cc1	number	1.5207926536
u0	number	0.998750444
u3	number	0.986550042
cc2	number	1.521
aa5	number	1.113
aa4	number	1.1125926536
aa1	number	0.5835926536
aa0	number	0.5836
aa3	number	1.1126
aa2	number	0.584
x2	number	881
c31	integer	16
c32	integer	1
a0	integer	16
a3	integer	20
bb0	number	1.0372
s5	number	0.8970286376
c3	integer	22
c2	integer	29
c1	integer	20
x1	number	369
c02	integer	1
x4	number	231
x5	number	569
p3	number	0.4423076923
p0	number	0.8344827586
r0	number	0.05
r3	number	0.1634615385
bb3	number	0.6224
t5	number	0.5826617543
t2	number	0.8608816879
t3	number	0.5829867936
t0	number	0.8609834318
u5	number	0.9866153469
c5	integer	23
cc4	number	1.4065926536
c01	integer	20
bb5	number	0.622
bb4	number	0.6223926536
check2	number	-0.0000073464
bb2	number	1.037
bb1	number	1.0371926536
check1	number	-0.0000073464

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.

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Generated value: `integer`

← Depends on:

→ Used by:

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Number entry
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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 $\var{b3}$ .

Give a worked solution to the whole question.

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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 2 years, 10 months ago

Newcastle University Mathematics and Statistics 9 years, 2 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 2 years, 10 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`