"A rope exerts a 40 N force on an object at an angle of 43^{\circ}43 ∘ above the horizontal. What are the components (horizontal and vertical) of the force."

Answer 1

I always start with a sketch. The hypotenuse is 40N, and the angle 43° above the x-axis. Adjacent side is the x component F_x and opposite side F_y. Cos 43° = F_x /40 and F_x = 40 (0.7660) = 30.6 N.

Sin 43° = F_y /40 and F_y = 40 (0.6428) = 25.7 N.

(math check: F_x² + F_y² should equal 40², allowing for roundoff error)