Two forces of magnitude 10N and 15N are acting at a point. The magnitude of their resultant is 20N. What is the angle between them?

 Two forces of magnitude 10N and 15N are acting at a point. The magnitude of their resultant is 20N. What is the angle between them?

Solution

This question can be answered by using the law of cosines in the form R^2 = a^2 + b^2 - 2ab * cos C where a^2 = 100 ; b^2 = 225 ; and angle C = (180 - 75.53) degrees or angle C = 104.48 degrees. Its supplementary angle is 75.53 degrees.

I used my vector addition computer program to solve for the resultant and the screenshot of the output screen in table form is shown below. The graphical output is also shown in a separate screenshot.

Vector a at 10 N is in blue, vector b at 15 N is in green and the red line is the 20 N resultant. The angle between the two given vectors is 75.53 degrees.