# Force vectors acted on by two forces

**1. The problem statement, all variables and given/known data**

A body is acted on by two forces. Find the magnitude and direction of the resultant force by using the mathematical method. I’m not sure if I’ve done this correctly, any pointers would be appreciated 🙂

Also what is the angle between the two vectors? Is it 90 or 76 degrees?

Not sure how to describe this in words so I have the image for the diagram.

http://ift.tt/1oxO7x6

**2. Relevant equations**

**3. The attempt at a solution**

Working out the first triangle.

x=cos45 x 90 = 63.64

y=sin^^^^^^^^^

Working out the second triangle.

x=cos45 x 10 = 7.07

y= sin^^^^^^^^

So for the system

x=63.64 + 7.07= 70.71

y= 63.64-7.07= 56.57

√70.71^2+56.57^2 = 90.554 N

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Direction

Tanθ = opp/adj

=70.71/56.57

=1.25

Tan-1 1.25 = 51.34° above the horizontal.

http://ift.tt/1qKcYkw