Find the resultant of `vec(F_(1)) + vec(F_(2)) - vec(F_(3)) ( sin 37^(@) = (3)/(5) , cos 37^(@) = (4)/(5))`

Explanation

`vec(R) = vec(F_(1)) + vec(F_(2)) - vec(F_(3)) = vec(F_(1)) + vec(F_(2)) + (-vec(F_(3)))`
Reverse the direction of `vec(F_(3))` and add vectors by the component approach.
`F_(x) = 5 F_(0) cos 37^(@) - 12 F_(0)`
` = 5 F_(0) xx (4)/(5) - 12 F_(0) = - 8 F_(0)`
`F_(y) = 5 F_(0) sin 37^(@) + 3 F_(0)`
` = 3 F_(0) xx (3)/(5) + 3 F_(0) = 6 F_(0)`
`F = sqrt((8 F_(0))^(2) + (6 F_(0))^(2)) = 10 F_(0)`
`tan theta = (6 F_(0))/( 8 F_(0)) = (3)/(4) rArr theta = 37^(@)`