Question

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Having lots of trouble with this question. I started with
150 (cos(30), sin(30)) + 75 (cos(150), sin(150))
F = 150 (√3/2, 1/2) + 75 (−√3/2, 1/2)
F = (75√3+37.5, 75+75√3/2)
But I'm having trouble finding the magnitude after that

Answer 1

You have messed up on your last line:

F = 150 (√3/2, 1/2) + 75 (−√3/2, 1/2)
F = (75√3-37.5√3, 75+75/2)
F = (37.5√3,112.5)
= 75 (√3/2,3/2)
= 75√3 (1/2,√3/2)
= 130 at 60°

Answer 2

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