Apply the sine rule

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

Name	Status	Author	Last Modified
Apply the sine rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
cormac's copy of Apply the sine rule	draft	cormac breen	24/10/2018 17:17

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Question statement

Suppose that $\Delta ABC$ is a triangle with $C> \dfrac{\pi}{2}$ (so it is an obtuse 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

s3	number	0.2514711974
cc0	number	1.6657
b0	integer	30
cc3	number	2.3603
b3	integer	20
cc2	number	1.666
check	number	-0.0000073464
q0	number	0.5903271693
q3	number	0.8642857143
cc5	number	2.360
s2	number	0.5115605559
s0	number	0.5112168161
cc1	number	1.6656926536
u0	number	0.9955000254
u3	number	0.7041977963
u2	number	0.9954715522
aa5	number	0.254
aa4	number	0.2541926536
aa1	number	0.5365926536
aa0	number	0.5366
aa3	number	0.2542
aa2	number	0.537
c31	integer	24
c32	integer	29
a0	integer	19
a3	integer	10
s5	number	0.2512776194
c3	integer	28
c0	integer	37
c02	integer	47
p3	number	0.9678571429
p0	number	0.8594594595
r0	number	-0.0947368421
r3	number	-0.71
bb3	number	0.5271
t5	number	0.502942649
t2	number	0.8069679087
t3	number	0.5030290784
t0	number	0.807145051
u5	number	0.7044107658
cc4	number	2.3602926536
c01	integer	37
bb5	number	0.527
bb4	number	0.5270926536
check2	number	-0.0000073464
bb2	number	0.939
bb1	number	0.9392926536
bb0	number	0.9393

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
sin(AA3)

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: `number`

0.2514711974

← 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.

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

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Apply the sine rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`