# Resultant of forces

From the illustration provided on the question, we have the angle between F₁ and F₂ to be 20 deg + 30 deg.

But using the formula R = F₁² +F₂² -2F₁F₂ Cosθ to get the Resultant, 130deg was used instead of 50deg as we have it in the illustration.

How did we get the 130deg?

• I'd guess 50° + 80N. Which is wrong! Should be cos 50°. Error in graphics arts department. – StainlessSteelRat Feb 18 at 16:33
• @Wasabi Always hated Law of Cosines! – StainlessSteelRat Feb 18 at 19:33
• 180 - 50 = 130. They did it to get the sign correct because they are too lazy to formulate the equation in a general way. This one requires you to use the interior angle of the parallelogram. These sort of ad-hoc methods will cause you trouble for the rest of your life. Unlearn them and replace with a suitable general method that doesn't force you to figure out whether you need to add or subtract angles on a case by case basis. – Phil Sweet Feb 18 at 23:57

The parallel to f1 is at an angle of 50 degrees with F2.

The angle opposite the resultant in the triangle with F2 and the parallel F1 is 130 degrees .

• To find the resultant of 2 vectors we assemble the tail of one to the head of the other one. Then the angle at this intersection $\theta = 130^0$ – kamran Feb 18 at 17:16

It's because of the way the Law of Cosines works. They get the answer in one calculation.

If you know $$a$$, $$b$$, and angle in between them $$\gamma$$, then you will get c. The magnitude to complete the triangle.

But to apply Law of Cosines to vector addition, you must put tail of one vector on tip of the other. This changes angle to (180° - $$\gamma$$). Now you get vector addition magnitude.