Two ropes in a vertical plane exert equal-magnitude
forces on a hanging weight but pull with an angle of 86.0° between
them. What pull does each one exert if their resultant pull is 372 N
directly upward?

--
ok so, I calculated that one of the ropes pulling on the mass with an angle of 43 deg would be 508 N
because i turned it into a right triangle and did the math where A sin 47 = 372 and evaluated rope A for 508.65 N, though the book solved it differently using: 372 = 2A cos 43 deg; instead. so, what have I been doing wrong?

Question

Two ropes in a vertical plane exert equal-magnitude
forces on a hanging weight but pull with an angle of 86.0° between
them. What pull does each one exert if their resultant pull is 372 N
directly upward?

--
ok so, I calculated that one of the ropes pulling on the mass with an angle of 43 deg would be 508 N
because i turned it into a right triangle and did the math where A sin 47 = 372 and evaluated rope A for 508.65 N, though the book solved it differently using: 372 = 2A cos 43 deg; instead. so, what have I been doing wrong?

anonymous · Answer

You did it correctly (with your geometry).

But you forgot that 372 N up is the resultant. So each contributes half that: 186 N.

A sin 47 = 186

should be correct

lanhikari22 · Answer

@Pompeii00  yeah, you're correct. for whatever reason, i've assumed that the resultant was on equal magnitude as the other two forced exerted by the rope. I've realized my mistake so thank you.