IGCSE Maths help

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Freestyleisa99
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#1
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#1
Could someone please help me understand how the rearrangement of the cosine rule works to find an angle. As well as this could you also explain how i know which part of the triangle resembles a,b or c???
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AgonizedGod
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Firstly, lets talk about your "a,b or c???" issue. The three sides of the triangle are named the Hypotenuse (Hyp), Opposite (Opp) and Adjacent (Adj). The Hyp will always be the LONGEST side of the triangle, the Adj is always the line in between the two angles and the Opp is always the remaining side (you can also remember it as the side opposite the Hyp) this is how I remember then.

Next, when you want to find the angle you use the inverse operation on your calculator by using the two numbers you've been given already and dividing one by the other. For example, if it was to cosine rule you're using you type the on your calculator Cos(to the power of -1) which can be typed by pressing shift on your scientific calculator and then pressing "Cos" Adjacent/Hypotenuse.

Now, the co-sine rule comes into effect when you have the Adjacent and Hypotenuse. You can remember what is what with the acronym SOHCAHTOA and as there are 9 letters every 3 form to make a formula triangle. SOH forms to make Opposite on the top with Sine and Hypotenuse on the bottom, CAH forms to make Adjacent on the top and Co-sine and Hypotenuse on the bottom and finally TOA make Opposite on the top and Tangent and Adjacent on the bottom. The middle letter of the three always goes on top.

Hope this helps and if it doesn't quite, just reply and I'll reply back ASAP.

Good luck for your exam!
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Freestyleisa99
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#3
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#3
(Original post by AgonizedGod)
Firstly, lets talk about your "a,b or c???" issue. The three sides of the triangle are named the Hypotenuse (Hyp), Opposite (Opp) and Adjacent (Adj). The Hyp will always be the LONGEST side of the triangle, the Adj is always the line in between the two angles and the Opp is always the remaining side (you can also remember it as the side opposite the Hyp) this is how I remember then.

Next, when you want to find the angle you use the inverse operation on your calculator by using the two numbers you've been given already and dividing one by the other. For example, if it was to cosine rule you're using you type the on your calculator Cos(to the power of -1) which can be typed by pressing shift on your scientific calculator and then pressing "Cos" Adjacent/Hypotenuse.

Now, the co-sine rule comes into effect when you have the Adjacent and Hypotenuse. You can remember what is what with the acronym SOHCAHTOA and as there are 9 letters every 3 form to make a formula triangle. SOH forms to make Opposite on the top with Sine and Hypotenuse on the bottom, CAH forms to make Adjacent on the top and Co-sine and Hypotenuse on the bottom and finally TOA make Opposite on the top and Tangent and Adjacent on the bottom. The middle letter of the three always goes on top.

Hope this helps and if it doesn't quite, just reply and I'll reply back ASAP.

Good luck for your exam!
Wasn't quite what i was asking, i have attached a picture of the question below. I was just wondering how i would label the sides based on the a,b,c lettering in the cosine rule. Also, if you could show me how i could re-arrange the formula to solve this question i would be very grateful,

ThanksImage!!!
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AgonizedGod
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I'm not sure how the answer this question as I've never seen it before with all three sides given. I can't help you there, sorry.

Anyway, good luck for your exam.
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nox1
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#5
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#5
I can help, you need to use a^2 = b^2 + c^2 - 2bc*cosA
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nox1
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#6
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#6
Okay so a, b and c can be any side. What matters is which angle they correspond to, A, B or C. Angle A will be opposite to side a. So in your picture, angle A is x and side a is the 8cm side.
Which side is b and c doesn't matter in the cosine rule.

You then plug the numbers into the equation:

82 = 42 + 62 - (2 x 4 x 6 x CosA)

You can then simplify it so that you get all the numbers on one side, and cosA on the other. You then put the number you get into cos-1 and that should be your answer!
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username1356366
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#7
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#7
Hi!

They should have the formula you wrote down on the formula sheet, but it's easier to remember the rearranged version.

Firstly, the rearranged formula is

Cos A = (b2 + c2 - a2) / 2bc.

The angle you want to find out is A, so the side opposite that would be a. Then, the others can be labelled however.

Let's say that the x = A , 8cm side is a, 4cm side is c and 6cm side is b.

So, (6^2 + 4^2 - 8^2) / (2x4x6) = cos A = -0.25.

Then, use cos^-1, so cos^-1(-0.25) = A = 104.5

Hope this helped
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username1560589
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#8
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#8
(Original post by Freestyleisa99)
Could someone please help me understand how the rearrangement of the cosine rule works to find an angle. As well as this could you also explain how i know which part of the triangle resembles a,b or c???
A is the angle opposite side a, B is opposite b, C is opposite c.
a^2 = b^2 +c^2 -2bc\cos A, which rearranges to \cos A = \dfrac{b^2+c^2-a^2}{2bc}

(Original post by AgonizedGod)
I'm not sure how the answer this question as I've never seen it before with all three sides given. I can't help you there, sorry.

Anyway, good luck for your exam.
You don't come across like you've heard of the cosine rule.
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Freestyleisa99
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#9
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#9
Thanks guys for the replies, i finally got there in the end!!!
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