Apply the sine rule

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 4 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	0.435505724
cc0	number	1.8059
b0	integer	22
cc3	number	2.2936
b3	integer	16
cc2	number	1.806
check	number	-0.0000073464
q0	number	0.7613636364
q3	number	0.9220430108
cc5	number	2.293
s2	number	0.5891447579
s0	number	0.5893871397
cc1	number	1.8058926536
u0	number	0.9724901965
u3	number	0.7499540776
u2	number	0.9724668973
aa5	number	0.450
aa4	number	0.4504926536
aa1	number	0.6302926536
aa0	number	0.6303
aa3	number	0.4506
aa2	number	0.630
c31	integer	26
c32	integer	32
a0	integer	20
a3	integer	18
s5	number	0.4349655341
c3	integer	31
c0	integer	33
c02	integer	40
p3	number	0.9002016129
p0	number	0.8078512397
r0	number	-0.2329545455
r3	number	-0.6614583333
bb3	number	0.3975
t5	number	0.3866534111
t2	number	0.6480338295
t3	number	0.3871144753
t0	number	0.6483384223
u5	number	0.7503508365
cc4	number	2.2934926536
c01	integer	31
bb5	number	0.397
bb4	number	0.3973926536
check2	number	-0.0001073464
bb2	number	0.705
bb1	number	0.7053926536
bb0	number	0.7054

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`

0.435505724

← 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.

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 4 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, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`