Question

Three forces with magnitudes of 55 pounds, 85 pounds, and 150 pounds act on an object at angles of 40 degrees,45 degrees, and 130 degrees, respectively, with the positive x-axis. Find the direction and magnitude of the resultant of these forces.

photo for reference

Answer 1

210.4∠88.4° pounds

Explanation:

The sum of the forces is ...

55∠40° +85∠45° +150∠130° =

55(cos(40°), sin(40°)) +85(cos(45°), sin(45°)) +150(cos(130°), sin(130°)) =

(42.132, 35.353) +(60.104, 60.104) +(-96.418, 114.907) =

(5.818, 210.364) = (√(5.818² +210.364²))∠arctan(210.364/5.818)

= 210.4∠88.4° . . . pounds