# Resolving 3 forces and finding resultant horizontal and vertical components

I have the question "Resolve the forces acting on the following objects into their vertical and horizontal components and thus find the vertical and horizontal components of their resultant force.

I have drawn a triangle from this.

And have worked out the net vertical and horizontal force.

I know I have to use trigonometry to solve this, however I am use to solving with only one side and one angle given.

In this case it will be two sides and one angle given.

8.0 N for the horizontal side of the triangle and 10.0N for the diagonal side of the triangle (the hypotenuse).

Is what I have done correct ? The final answer when I checked the solutions for the resultant force should be Zero resultant force.

However, I am unsure on how this is achieved.

The horizontal component would be $10\cos (36.87^\circ) N \approx 8N$ to the left.
The vertical component would be $10\sin (36.87^\circ) N \approx 6N$ towards upward direction.
• We can replace the $10N$ diagonal vector with $2$ vectors. Erase it and replace it with $2$ vectors, one vector point to the left with a vector of $8N$ to the left and another vector that points upwards with magnitude $6N$. – Siong Thye Goh Jan 18 '17 at 19:41