Answer to Question #231748 in Physics for Arisco

Question

A force of 5N is inclined at 45 degrees to a horizontal force of 8N. Find the magnitude of the resultant force and its direction?

Answer 1

Sketch the diagram:

Find the x- and y-components:

$$R_x=8+5\cos45=11.54\text N.\\ R_y=0+5\sin45=3.54\text N.\\ R=\sqrt{R_x^2+R_y^2}=12.1\text N.\\\space\\ \theta=\arctan\frac{R_y}{R_x}=17°.$$