resultant force

Question

Apoint is pulled by two ropes: one to the left and up 34 degrees with a magnitude of 5, the other to the right and up 16 degrees with a magnitude of 7.  What is the resultant force on the point?

Answer 1

Taking +x as right and +y as up,

 

F_x = -5cos34° + 7cos16° ≅ 2.584 

 

F_y = 5sin34° + 7sin16° ≅ 4.725

 

F = √(F_x² + F_y²)

 

The angle F makes from the +x direction is

 

θ = arctan(F_y/F_x)

 

Note that θ must be in quadrant I since both F_x and F_y > 0.  You can finish from here.