Apply the sine rule

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Mohammad Rahman

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Ready to use

2 years, 11 months ago

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Mohammad Rahman 2 years, 11 months ago

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Newcastle University Mathematics and Statistics 9 years, 4 months ago

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Name	Status	Author	Last Modified
Apply the sine rule	Ready to use	Newcastle University Mathematics and Statistics	25/06/2022 13:25
cormac's copy of Apply the sine rule	draft	cormac breen	24/10/2018 13:53
Apply the sine rule (2 angles, 1 side, degrees)	Ready to use	Andrew Chuter	09/04/2020 05:29

There are 9 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 angles and a side length, determine the other two side lengths and the angle. Write down the side lengths as whole numbers and the angle (in radians) as a decimal to 3dp.

Give any introductory information the student needs.

			Name	Type	Generated Value

c4	integer	15
s3	number	0.4670928011
cc0	number	1.4827
temp2	number	0.0004445968
temp1	number	24.9995554032
b0	integer	25
cc3	number	1.2062
b3	integer	17
u2	number	0.9961483775
q0	number	0.4571428571
q3	number	0.12109375
c0	integer	28
cc5	number	1.206
s2	number	0.5337255691
s0	number	0.5336410007
cc1	number	1.4826926536
u0	number	0.9961220276
u3	number	0.9342677759
cc2	number	1.483
aa5	number	0.486
aa4	number	0.4859926536
aa1	number	0.5628926536
aa0	number	0.5629
aa3	number	0.4860
aa2	number	0.563
x2	number	850
c31	integer	15
c32	integer	1
a0	integer	15
a3	integer	8
bb0	number	1.0960
s5	number	0.4670928011
c3	integer	16
c2	integer	29
c1	integer	20
x1	number	400
c02	integer	1
x4	number	225
x5	number	353
p3	number	0.8841911765
p0	number	0.8457142857
r0	number	0.088
r3	number	0.3566176471
bb3	number	1.4494
t5	number	0.9925919919
t2	number	0.8893858508
t3	number	0.9926405107
t0	number	0.8893858508
u5	number	0.9341964428
c5	integer	18
cc4	number	1.2061926536
c01	integer	20
bb5	number	1.449
bb4	number	1.4493926536
check2	number	-0.0000073464
bb2	number	1.096
bb1	number	1.0959926536
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.

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 Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

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

$A=\var{AA0}$ , $B=\var{BB0}$ , $a=\var{a0}$

Side length $b=$ Gap 0.

Angle $C=$ Gap 1.

Side length $c=$ Gap 2.

Advice

a) We use the Sine Rule to find $b$ : $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$ . Thus $b=\dfrac{a \sin B}{\sin A}=\dfrac{\var{a0}* \var{t0}}{\var{s0}}=\var{a0*t0/s0}$ . The closest integer is then $\var{b0}$ .

Since $A+B+C=\pi$ , we calculate $C=\pi-A-B=\var{CC1}$ . To 3dp, this gives $\var{CC2}$ .

We use the Sine Rule to find $c$ : $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$ . Thus $c=\dfrac{a \sin C}{\sin A}=\dfrac{\var{a0}* \var{u2}}{\var{s0}}=\var{a0*u2/s0}$ . The closest integer is then $\var{c0}$ . Note that this solution uses the 3dp value of $C$ ; the answer using $\var{CC1}$ would give a slightly different long decimal value of $c$ , but the integer value would be the same.

b) We use the Sine Rule to find $b$ : $\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$ . Thus $b=\dfrac{c \sin B}{\sin C}=\dfrac{\var{c3}* \var{t3}}{\var{u3}}=\var{c3*t3/u3}$ . The closest integer is then $\var{b3}$ .

Since $A+B+C=\pi$ , we calculate $A=\pi-B-C=\var{AA4}$ . To 3dp, this gives $\var{AA5}$ .

We use the Sine Rule to find $a$ : $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$ . Thus $a=\dfrac{c \sin A}{\sin C}=\dfrac{\var{c3}* \var{s5}}{\var{u3}}=\var{c3*s5/u3}$ . The closest integer is then $\var{a3}$ . Note that this solution uses the 3dp value of $A$ ; the answer using $\var{AA4}$ would give a slightly different long decimal value of $a$ , but the integer value would be the same.

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?
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Information only
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

Checkpoint description

Mohammad Rahman 2 years, 11 months ago

Newcastle University Mathematics and Statistics 9 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Apply the sine rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mohammad Rahman 2 years, 11 months 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`