complex numbers

[granite shadow]

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[distant axle]

basically a drew arg 18 with side length 5. and arg 72

i connected it to make a parallelogram

with arg w + z bisecting the middle of it

+close

[mortal sandal]

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[heavy oasis]

That's not correct.

[distant axle]

uh what do i do

when i mean by bisecting

it goes

through the corners

like in that

72 degree angle

[heavy oasis]

Oh. Well, that's not bisecting, that's just the diagonal of this parallelogram. In that case it's correct.

The rest can just be done using geometry.

[distant axle]

well what i did was i got a triangle with angles18 54 and 108

and one side length as 5

i did 5 sin(108) / sin 54. but it doesnt match the mark scheme

@heavy oasis

[heavy oasis]

Can you show your picture?

[distant axle]

uh yeah sure

[distant axle]

here

lemme rotate

+wait

i forgot cmd

[distant axle]

+rotate

...

lemme

do smth

[heavy oasis]

Let's make the picture a bit simpler.
We know |w|, θ1, θ2 and φ, and we need to find |z|.

So, the bottom-left angle is, of course, (φ - θ1). What about the bottom-right one?

[distant axle]

uh do you do 72 - 18 and since they are co interior its 180 - 54 idrk

which is like 126

[heavy oasis]

Yes. In other words, π - θ2 + θ1.

And, knowing these two angles, what's the top-right angle?

[distant axle]

uh 36?

[heavy oasis]

Yeah, nice! In other words, θ2 - φ.
And now you can use sine theorem.

[distant axle]

for some reason the mark scheme

says

5 sin (pi / 10) / sin(pi / 5)

[heavy oasis]

Yes.

Which is what you'll get.

Assuming you apply sine theorem correctly, of course.

[distant axle]

huh

wait so the angles are 36 18 and 126 right

so 5/sin(36) = x / sin(126)

5 sin(126) / sin(36)

[heavy oasis]

All in degrees. Don't forget to write the degree sign.

[distant axle]

yeah i know

[distant axle]

but

that says 5 sin(18) / sin(36)

[heavy oasis]

This is incorrect.

You took the wrong angle for the right side.

What angle lies opposite of z?

[distant axle]

wait why are we looking at z

i dont think we know z's length

only w

is given

which has a length of 5

[heavy oasis]

Because we're asked to find it...

[distant axle]

OH

bro i was solving

for w + z

[heavy oasis]

Oh, I see.

[distant axle]

+close

[mortal sandal]

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