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.

Answer 1

F_x = 150cos 30 - 75cos 30 = 64.95
F_y = 150sin 30 + 75sin 30 = 112.5

R = sqrt(64.95^2 + 112.5^2) = sqrt(16874.75) = 129.90
Direction of R is arctan(112.5/64.95) = arctan(1.73) = 59.97°