Katy's Apply the sine rule

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Katy Dobson 6 years, 8 months ago

Created this as a copy of Apply the sine rule.

Name	Status	Author	Last Modified
Apply the sine rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Katy's Apply the sine rule	draft	Katy Dobson	08/08/2018 10:08
Apply the sine rule (1 angle, 2 sides, degrees)	Ready to use	Andrew Chuter	08/04/2020 13:13

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 angle and two side lengths, use the Sine Rule to determine the other side length and two angles. Write down the side length as a whole number and the angles (in radians) as decimals to 3dp.

Give any introductory information the student needs.

			Name	Type	Generated Value

c4	integer	16
s3	number	0.9989652206
cc0	number	0.7227
temp2	number	-0.0000579149
temp1	number	20.0000579149
b0	integer	20
cc3	number	0.9996
b3	integer	11
u2	number	0.6616371185
bb51	number	0.616
q0	number	0.5625
q3	number	0.8157894737
c0	integer	16
aa4	number	1.5252926536
cc5	number	1.000
s2	number	0.9920980708
s0	number	0.9921606792
cc1	number	0.7226926536
u0	number	0.6614121415
u3	number	0.8412547966
cc2	number	0.723
aa5	number	1.525
cc21	number	0.723
aa1	number	1.4454926536
aa0	number	1.4455
aa3	number	1.5253
aa2	number	1.445
x2	number	976
c31	integer	16
c32	integer	1
bb01	number	0.973
t51	number	0.5777750071
a0	integer	24
a3	integer	19
bb0	number	0.9734
s4	number	0.9989900709
s5	number	0.9989515315
c3	integer	16
c2	integer	31
c1	integer	14
x1	number	176
bb41	number	0.6159926536
x4	number	240
x5	number	482
p3	number	0.0454545455
p0	number	0.125
r0	number	0.75
r3	number	0.5406698565
bb3	number	0.6167
aa31	number	1.526
t5	number	0.5785909142
t2	number	0.8265778974
t3	number	0.5783462028
t0	number	0.8268029602
t1	number	0.826800566
u5	number	0.8414709848
c02	integer	1
c5	integer	21
u21	number	0.6616371185
cc4	number	0.9995926536
cc11	number	0.7230926536
c01	integer	14
bb5	number	0.617
bb4	number	0.6166926536
check2	number	-0.0000073464
bb2	number	0.973
bb1	number	0.9733926536
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
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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.

$A=\var{AA0}$ , $a=\var{a0}$ , $b=\var{b0}$

Angle $B=$ 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 $\sin B=\dfrac{b \sin A}{a}=\dfrac{\var{b0}* \var{s0}}{\var{a0}}=\var{b0*s0/a0}$ . To find $B$ we need to calculate $\sin^{-1} (\var{b0*s0/a0})$ , calculating the angle between $0$ and $\dfrac{\pi}{2}$ , so $B=\var{bb01}$ (to 3 decimal places).

Since $A+B+C=\pi$ , we calculate $C=\pi-A-B=\var{CC11}$ . To 3dp, this gives $\var{CC21}$ .

We use the Sine Rule to find $c$ : $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$ . Thus $c=\dfrac{a \sin C}{\sin A}=\dfrac{\var{a0}* \var{u21}}{\var{s0}}=\var{a0*u21/s0}$ . The closest integer is then $\var{c0}$ . Note that this solution uses the 3dp value of $C$ ; the answer using $\var{CC11}$ 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 $A$ : $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$ . Thus $\sin A=\dfrac{a \sin C}{c}=\dfrac{\var{a3}* \var{u3}}{\var{c3}}=\var{a3*u3/c3}$ . To find $A$ we need to calculate $\sin^{-1} (\var{a3*u3/c3})$ , calculating the angle between $0$ and $\dfrac{\pi}{2}$ , so $A=\var{aa31}$ (to 3 decimal places).

Since $A+B+C=\pi$ , we calculate $B=\pi-A-C=\var{bb41}$ . To 3dp, this gives $\var{bb51}$ .

We use the Sine Rule to find $b$ : $\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$ . Thus $b=\dfrac{c \sin B}{\sin C}=\dfrac{\var{c3}* \var{t51}}{\var{u3}}=\var{c3*t51/u3}$ . The closest integer is then $\var{b3}$ . Note that this solution uses the 3dp value of $B$ ; the answer using $\var{bb41}$ would give a slightly different long decimal value of $b$ , but the integer value would be the same.

Give a worked solution to the whole question.

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This question is used in the following exam:

NUMBAS - Sine and Cosine rules by Katy Dobson in Katy's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Katy Dobson 6 years, 8 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Katy's Apply the sine rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Katy Dobson 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`