find the resultant force magnitude and angle from adding f1f

find the resultant force magnitude and angle from adding f1+f2+f3
160 lbs at 45 degrees
90 lbs at 100 degrees
105 lbs at 290 degrees

f1 = 160 cos 45^o i + 160 sin 45^o j

= 160 (1/ square root of 2) i + 160 (1/ square root of 2) j

= 160(0.707) i + 160 (0.707) j = 113.13 i + 113.13 j

f2 = 90 cos 100^o i + 90 sin 100^o j

= 90 ( -0.173) i + 90 ( 0.984) j

= -15.628 i + 88.63 j

f3 = 105 cos 290^o i + 105 sin 290^o j

= 105(0.342) i + 105( -0.939)j

= 35.91 i - 98.66 j

resultant force is f =f1 + f2 + f3

= 113.13 i + 113.13 j + -15.628 i + 88.63 j + 35.91 i - 98.66 j

= i( 113.13 -15.628 +35.91 ) + j(113.13+88.63- 98.66)

resultant force, f = 133.412 i + 103.1 j

magnetude of f is square root of (133.412² + 103.1²)

= square root of ( 17798.76 + 10629.61) = 168.6

angle of f is tan^-1( 103.1 / 133.412)

= 37.69^o

therfore, the resultant force has a magnetude of 168.6, at an angle of 37.69 degrees.