Trigonometry Word Problem About Forces acting on a point

Question

Forces of 15 and 24 kg act on a point at an angle of 62owith respect to each other. Find the magnitude of the resulting force and the angles the resultant force makes with the given forces.

Answer 1

Trigonometrically, we analyze this by adding the two forces; thus, we have a triangle of lengths 15 and 24 and an included angle of 180 - 62 = 118 degrees.

The cosine law gives us the resultant force:

F = sqrt(15^2+24^2 - 2 * 15 * 24 * cos(118 degrees)) = 33.75

The angle with the 15 pound force will be arcsin(24/33.75*sin(118 degrees)) = 38.89°

The angle with the 24 pound force is arcsin(15/33.75*sin(118 degrees)) = 23.11°

Note that the two angles sum to 62º.