cosine

[slender ocean]

y does sine rule not work. 2 pairs of side + angle? i can see the cosine rule but y is it cosine not sine rule

[cold maple]

It does, this angle isnt 100 degrees though

If it was, R would be directly south of P when it isnt

Also youd have a triangle with sum of angles >180

And if you see on the diagram your x is shorter than 28, when it shouldnt be

You can get the angle tho, with some more sin rule as
28/siny = 12/sin(75-y)
where y is that angle, though this would become a bit of a mess if you dont know the needed trig identities (ones not given at gcse)

[cold maple]

Here you use cosine rule, as the angle is in between the 2 known sides - when it is not in between them, then you use sin rule (cosine rule would still work but youd get a quadratic to solve instead of the typical solution)

[slender ocean]

thank u so much ive never looked into the depths of the question like u do 🙏 this inspired me ong bc y did i think 100 + 105 was correct 💀

[slender ocean]

wait why does 180 - 80 not work here what have i got confused ab angles on a straight line add up to 180

[cold maple]

you got this angle correct if thats what you mean

but that doesnt mean the one in the triangle is also 100 degrees

[slender ocean]

yes but why wouldnt the same thing work with the angle i got wrong

[cold maple]

am i confusing what you mean, this isnt a straight line

[slender ocean]

i dont rlly understand why its not a straight line bc theres a straight line under it … 😭

ik what im thinking is wrong but idk why

[cold maple]

do you mean why B is a straight line but A isnt (well the bottom line i mean, not the one going up)?

[slender ocean]

Yeah i get it now thanks so they js dont lie on the same straight line

u said it earlier its not P to R south

ty man 🙏

[cold maple]

np