Apply the cosine rule

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

Feedback

From users who are not members of Content created by Newcastle University :

Anna Cartlidge

said

Needs to be tested

3 years ago

History

○

Anna Cartlidge 3 years ago

Gave some feedback: Needs to be tested

○

Newcastle University Mathematics and Statistics 9 years, 4 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	7
s3	number	0.6470431872
cc0	number	1.1800
temp2	number	0.0007521286
temp1	number	20.9992478714
b0	integer	21
cc3	number	1.5673
b3	integer	13
u2	number	0.9246060124
q0	number	0.380952381
q3	number	0.6443850267
c0	integer	21
cc5	number	1.567
s2	number	0.7046998388
s0	number	0.7044869554
cc1	number	1.1798926536
u0	number	0.9246060124
u3	number	0.9999938879
cc2	number	1.180
aa5	number	0.704
aa4	number	0.7036926536
aa1	number	0.7815926536
aa0	number	0.7817
aa3	number	0.7037
aa2	number	0.782
x2	number	697
c31	integer	7
c32	integer	1
a0	integer	16
a3	integer	11
bb0	number	1.1800
s5	number	0.6472718941
c3	integer	17
c2	integer	26
c1	integer	14
x1	number	185
c02	integer	1
x4	number	48
x5	number	290
p3	number	0.7624434389
p0	number	0.7097505669
r0	number	0.380952381
r3	number	0.0034965035
bb3	number	0.8706
t5	number	0.7649733813
t2	number	0.9246060124
t3	number	0.7647156954
t0	number	0.9246060124
u5	number	0.999992794
c5	integer	17
cc4	number	1.5672926536
c01	integer	14
bb5	number	0.871
bb4	number	0.8705926536
check2	number	-0.0000073464
bb2	number	1.180
bb1	number	1.1798926536
check1	number	-0.0001073464

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 $\var{b3}$ .

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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

This question is used in the following exams:

David's copy of Foundation mathematics by David Rickard in David's workspace.
Foundation mathematics by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Sine and Cosine Rule by Gareth Woods in Gareth's workspace.
Foundation mathematics quiz by Simon Thomas in Foundation mathematics.
Maria's copy of Foundation mathematics by Maria Aneiros in Maria's workspace.
Ann's copy of Foundation mathematics by Ann Smith in Foundation Maths.
Week 5 Review Quiz by John Harvey in Swansea MA-004.
Testing 1 by Niall Barr in Niall's workspace.
Ben's copy of Foundation mathematics by Ben Sathuluri in Ben's workspace.
Sine and Cosine Rule Exam by Michael O'Connor in Glasgow Numbas Question Pool.
Foundation of Maths by Chris Templet in Chris's workspace.
Robert's copy of Foundation mathematics by Robert Barham in Robert's workspace.
claire's copy of Foundation mathematics by claire lines in claire's workspace.
Week 5 by Pascal Buenzli in Trig.
A Test Exam by Niall Barr in Niall's workspace.

Loading...

Error

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, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

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, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`