resultant force

Two forces, P and Q, are such that the sum of their magnitudes is 45 N. The
resultant of P and Q is perpendicular to P and has a magnitude of 15 N.
Calculate:
(i) the magnitude of P and Q,
(ii) the angle between P and Q.

I get to the point where I have 3 equations:
1) P + Q = 45
2) Qsinx = 15
3) Qcosx - P = 0

I don't know how to resolve from here. Anyone able to help.

Thanks

Two forces, P and Q, are such that the sum of their magnitudes is 45 N. The
resultant of P and Q is perpendicular to P and has a magnitude of 15 N.
Calculate:
(i) the magnitude of P and Q,
(ii) the angle between P and Q.

I get to the point where I have 3 equations:
1) P + Q = 45
2) Qsinx = 15
3) Qcosx - P = 0

I don't know how to resolve from here. Anyone able to help.

Thanks

Try using Pythagoras instead of SOHCAHTOA.

3rd eq gives $Q \cos x = P$. Now you can use this and the second equation to say that $Q^2 \sin^2 x + Q^2 \cos^2 x = 15^2 + P^2$

Can you move from there?? This eq has an obvious identity you can use.

Thanks, can't believe I missed that!

I only have one value though so how can I do that?

So you're good to find the values now?

I only have one value though so how can I do that?