Two forces of 27 pounds and 62 pounds act on a body so that the resultant is a force of 76 pounds. Find, to the nearest degree, the angle between the resultant and the larger force.

Answer 1

By cosine law: 27² = 62² + 76² - 2·62·76cos∝; cos∝ = 8891/9424;

∝ = cos^-1(8891/9424) = 19°

Answer 2

We normally write the cosine law

c² = a²+ b² - 2ab cos C, but with a little bit of algebra, we can rewrite this first as

2ab cos C = a²+ b² - c² , then as

C = cos^-1((a²+ b² - c²)/2ab)

Written this way, we are solving for the angle in terms of the lengths.

We get C = cos^-1((27²+ 62² - 76²)/(2*27*62)) = cos^-1(-0.359318996415771) = 111°