Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

F = 150 (cos(30), sin(30)) + 100 (cos(120), sin(120))
F = 150 (sq3/2, 1/2) + 100 (−1/2, sq3/2)
F = (75sq3−50, 75+50sq3)

Magnitude of resultant force
= sq((75sq3−50)^2 + (75+50sq3)^2)
= sq32500
= 50sq13
≈ 180.278 pounds

Direction of resultant force
= tan^-1((75+50sq3)/(75sq3−50))
≈ 63.69 degrees
I was just wondering if this was correct...