Sine and Cosine to find area of surface.

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Whynotdd
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#1
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#1
I am struggling with this one, finding the area of the land via the sine or cosine rule. I just don't see how I can go about it, I know I could use the formula for the area of a non-right angled triangle if I split it from B to D and make two trianges (½ ab sin C) However, I don't see how I can use the sine rule and apply it. Any assistance would be appreciated.
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the bear
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#2
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#2
you need to split this quadrilateral into two triangles from B to D then use 1/2abSinC.

no need for the Sine Rule
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Whynotdd
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#3
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(Original post by the bear)
you need to split this quadrilateral into two triangles.
That is exactly what I thought, its not possible to use it either is it?
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the bear
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#4
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#4
i think you are perhaps mistaking "sine rule" for "use the area formula which mentions the sine" ?
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MezmorisedPotato
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#5
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#5
1/ If you draw a line BD, then you can use 1/2*A*B*SinC. i.e, 1/2*146.3*87*Sin120 and also 1/2*263.5*198.7*Sin60.
2/ Then add them together. As long as you have two sides enclosed in an angle, you can use the formula 1/2ABSinC.
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RDKGames
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#6
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#6
(Original post by Whynotdd)
That is exactly what I thought, its not possible to use it either is it?
Sine rule helps you find an angle or a length in a triangle, nothing to do with its area.
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have
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#7
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#7
(Original post by Whynotdd)
That is exactly what I thought, its not possible to use it either is it?
That way is the easiest way to do it. There probably is a way to do it using sine rule, but the question is why would you?
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MezmorisedPotato
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#8
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(Original post by the bear)
i think you are perhaps mistaking "sine rule" for "use the area formula which mentions the sine" ?
The area for triangle formula 1/2ABSinC is a derivation of the sine rule so it is technically the sine rule for area of triangles. Think that is what they meant.
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Whynotdd
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#9
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#9
(Original post by MezmorisedPotato)
1/ If you draw a line BD, then you can use 1/2*A*B*SinC. i.e, 1/2*146.3*87*Sin120 and also 1/2*263.5*198.7*Sin60.
2/ Then add them together. As long as you have two sides enclosed in an angle, you can use the formula 1/2ABSinC.
Yes, I know which Is what I am using but the questions specifically asks for sine or cosine rule which I dont see how you do it.
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MezmorisedPotato
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#10
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#10
(Original post by Whynotdd)
Yes, I know which Is what I am using but the questions specifically asks for sine or cosine rule which I dont see how you do it.
The area rule 1/2ABSinC is a derivation of the sine rule. They are based on each other so you are essentially using a version of the sine rule.
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the bear
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#11
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(Original post by Whynotdd)
Yes, I know which Is what I am using but the questions specifically asks for sine or cosine rule which I dont see how you do it.
well if you insist:

find BD using the Cosine Rule. then you have all the sides of the triangles and can then use Heron's Rule to find the two areas.
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Whynotdd
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#12
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#12
(Original post by StayWoke)
That way is the easiest way to do it. There probably is a way to do it using sine rule, but the question is why would you?
Thats what the question is asking for haha. It boggles me.
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Whynotdd
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#13
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#13
(Original post by MezmorisedPotato)
The area rule 1/2ABSinC is a derivation of the sine rule. They are based on each other so you are essentially using a version of the sine rule.
I will have to outsmart my tutor with that comeback then
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Whynotdd
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#14
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#14
(Original post by the bear)
well if you insist:

find BD using the Cosine Rule. then you have all the sides of the triangles and can then use Heron's Rule to find the two areas.
Thank you very much
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Whynotdd
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#15
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#15
(Original post by the bear)
i think you are perhaps mistaking "sine rule" for "use the area formula which mentions the sine" ?
No it says use the sine or cosine rule to measure the area of the land.
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MezmorisedPotato
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#16
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#16
(Original post by Whynotdd)
I will have to outsmart my tutor with that comeback then
Hahahaha
I am quite sure that is what they mean in the question, otherwise it seems like quite a long winded process which can be a pain!
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MezmorisedPotato
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#17
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(Original post by the bear)
well if you insist:

find BD using the Cosine Rule. then you have all the sides of the triangles and can then use Heron's Rule to find the two areas.
I just looked up this formula and it is actually so amazing Can't believe no one taught it to me in the past!
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Whynotdd
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#18
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#18
(Original post by MezmorisedPotato)
I just looked up this formula and it is actually so amazing Can't believe no one taught it to me in the past!
Yeah, I know. I knew it for a while but when he said specifically to use the sine rule it hurt my head cause I couldnt see the way to do it.
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the bear
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#19
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#19
(Original post by Whynotdd)
No it says use the sine or cosine rule to measure the area of the land.

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Whynotdd
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#20
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#20
(Original post by the bear)


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haha
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