Apply the sine rule

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Mohammad Rahman

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Ready to use

2 years, 10 months ago

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Mohammad Rahman 2 years, 10 months ago

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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 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

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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	10
s3	number	0.8333273726
cc0	number	0.3011
temp2	number	0
temp1	number	10
b0	integer	10
cc3	number	0.5890
b3	integer	18
u2	number	0.2964753952
q0	number	0.15
q3	number	0.0033333333
c0	integer	3
cc5	number	0.589
s2	number	0.9886517629
s0	number	0.9886817882
cc1	number	0.3011926536
u0	number	0.2965708978
u3	number	0.5555298042
cc2	number	0.301
aa5	number	0.985
aa4	number	0.9850926536
aa1	number	1.4202926536
aa0	number	1.4202
aa3	number	0.9851
aa2	number	1.420
x2	number	200
c31	integer	10
c32	integer	1
a0	integer	10
a3	integer	15
bb0	number	1.4202
s5	number	0.8332720904
c3	integer	10
c2	integer	14
c1	integer	1
x1	number	0
c02	integer	1
x4	number	99
x5	number	549
p3	number	0.5527777778
p0	number	0.15
r0	number	0.955
r3	number	0.8314814815
bb3	number	1.5675
t5	number	0.999992794
t2	number	0.9886517629
t3	number	0.9999945671
t0	number	0.9886817882
u5	number	0.5555298042
c5	integer	23
cc4	number	0.5889926536
c01	integer	0
bb5	number	1.567
bb4	number	1.5674926536
check2	number	-0.0000073464
bb2	number	1.420
bb1	number	1.4202926536
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 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
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Gap-fill

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

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

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

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Comment

Checkpoint description

Mohammad Rahman 2 years, 10 months ago

Newcastle University Mathematics and Statistics 9 years, 3 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, 10 months 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`