Add the following vectors:
440 N at 100 degrees
905 N at 160 degrees
A.1187.7 N at 128.7 degrees
B.1010.4 N at 48.2 degrees
C.1345 N at 130 degrees
D.1013.5 N at 149 degrees
you can get easy conversions at wolframalpha.com
Just enter you polar values, and you can read off the Cartesian ones. For example,
http://www.wolframalpha.com/input/?i=440+cis+100%C2%B0
It shows the polar value as a complex number, but that's just the x- and y-components.
No doubt there are other handy conversion sites as well. Of course, you could just use your calculator...
To add the given vectors, you need to break each vector into its horizontal and vertical components.
For the first vector, 440 N at 100 degrees, the horizontal component can be found by multiplying the magnitude (440 N) by the cosine of the angle (100 degrees). The vertical component can be found by multiplying the magnitude by the sine of the angle.
For the second vector, 905 N at 160 degrees, the same process applies: multiply the magnitude (905 N) by the cosine of the angle (160 degrees) to find the horizontal component, and multiply the magnitude by the sine of the angle to find the vertical component.
Once you have the horizontal and vertical components of both vectors, you can add them separately. The horizontal components are added together, and the vertical components are added together.
Finally, you can combine the resultant horizontal and vertical components to find the magnitude and angle of the resultant vector.
Let's calculate:
For the first vector:
Horizontal component = 440 N * cos(100 degrees)
Vertical component = 440 N * sin(100 degrees)
For the second vector:
Horizontal component = 905 N * cos(160 degrees)
Vertical component = 905 N * sin(160 degrees)
Next, add the horizontal components together:
Total horizontal component = Horizontal component of first vector + Horizontal component of second vector
Add the vertical components together:
Total vertical component = Vertical component of first vector + Vertical component of second vector
Now, to calculate the magnitude and direction of the resultant vector, use the Pythagorean theorem:
Magnitude = sqrt((Total horizontal component)^2 + (Total vertical component)^2)
Direction = arctan(Total vertical component / Total horizontal component)
Calculate the magnitude and direction to find the answer to the question.