[dannylfc_1]

Hi guys,

If I have a triangle, of which I know all the sides (I'm working with complex numbers) im trying to work out the ARGUMENT i.e arctan (y/x) without a calculator.
This is just the angle between my hypotenuse which is 2 root 2 and my adjacent which =2. Opposite is also 2.

How can I do this?

Thanks, really stuck.

[Bobifier]

If you're looking for angles, you want to start with the cosine rule. Square all the sides and look at what that tells you.

[Joinedup]

That's half a right angle.

[tazarooni89]

Sounds like you're dealing with a right-angled isosceles triangle (i.e. half a square) - since the opposite and adjacent are both 2, and the triangle obeys Pythagoras' theorem.
Should be obvious what the angle is...

[pauching]

Isn't the answer: arg= tan^-1 1= (pi)/4 = 45^o

[dannylfc_1]

Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

Thanks

[TheMagicMan]

(Original post by dannylfc_1)
Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

Thanks

It's been suggested...the cosine rule. In general for a triangle with integral sides the angles will not be rational

[DFranklin]

(Original post by dannylfc_1)
Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3.

These is no general method that will work for everything.

You should know (*) the values of for any integer multiple of or .

All the examples you have given fall into this category, and this is likely no coincidence.

(*) Or be able to work out from a value you do know. e.g. I might not know directly what sin(3pi/4) is, but I know that sin(3pi/4) = sin(pi - 3pi/4) = sin(pi/4) = sqrt(2)/2.

[pauching]

(Original post by dannylfc_1)
Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

Thanks

okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?

[dannylfc_1]

(Original post by pauching)
okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?

yes sorry - the angle between adjacent and hypotenuse.
I see the cosine rule has been mentioned but can someone spell this out for me exactly how you work it out. Maths isn't my strongest subject!

[dannylfc_1]

(Original post by DFranklin)
These is no general method that will work for everything.

You should know (*) the values of for any integer multiple of or .

All the examples you have given fall into this category, and this is likely no coincidence.

(*) Or be able to work out from a value you do know. e.g. I might not know directly what sin(3pi/4) is, but I know that sin(3pi/4) = sin(pi - 3pi/4) = sin(pi/4) = sqrt(2)/2.

Yes, I understand, so how then do I work out arctan? Thanks

[DFranklin]

If you know the values for sin and cos, you know the value for tan...

[TheMagicMan]

(Original post by dannylfc_1)
yes sorry - the angle between adjacent and hypotenuse.
I see the cosine rule has been mentioned but can someone spell this out for me exactly how you work it out. Maths isn't my strongest subject!

In a triangle where the side of length is opposite angle A,

[dannylfc_1]

(Original post by pauching)
okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?

I also should have said minus root 3 not root 3

Its because my complex number is z=1-i root 3 and i want to put this in the form re^i(theta). Where r is the hypotenuse which is 2 and theta is the angle arctan. Hope that helps

[AverageExcellence]

A squared = B squared + C squared - (2BC) x Cos A

just rearrange the formula to make cos A the subject of the equation and you can work out each one

[dannylfc_1]

Yes thanks, i understand the cosine rule method. Thanks everyone for helping really appreciated

[DFranklin]

Have to say, I strongly disagree with everyone advocating the use of the cosine formula.

[dannylfc_1]

(Original post by DFranklin)
Have to say, I strongly disagree with everyone advocating the use of the cosine formula.

How else would you do it? I realise I'm getting to the point where I have cos A = x. But then I still need to know how to do the next part in my head, to which I think i might just have to memorise the unit circle.

[DFranklin]

If you have a right angled triangle, you don't need the cosine formula. This is basic (GCSE, I would have thought) trig.

[dannylfc_1]

True