Compute the resultant of the following coplanar forces?

Question

Compute the resultant of the following coplanar forces: 100 N at 30 degrees, 141.4N at 45 degrees, and 100 N at 240 degrees

Please show the steps of how you get the answer

Answer 1

1. First thing first: DRAW A PICTURE!!

2. Find the x and y components of each vector using trig

    a. for vector 100N @ 30deg. x=100cos30 and y=100sin30

    b. for vector 141.4N @45deg. x=141.4cos45 and y=141.4sin45

    c. for vector 100N @240deg. x=100cos240 and y=100sin240

3. Now, simply add up the values that you get for your x's and y's. This      

    will give you the x and y components of your resultant vector. I get

    that the x component is 136.58N and the y component is 63.38N.

4. Now use Pythagorean theorem to solve for the hypotenuse which is

    the magnitude of your resultant vector. I get 150.56N.

5. Now use some more trig and the tangent function to solve for the  

    angle. I get 24.89deg.