Vectors

Q3. The resultant of two forces is 60 N. It acts at an angle of 30° to one of the forces, which has a magnitude of 45 N.

Find the magnitude of the second force.

To tackle the problem by calculation we can use the cosine rule

a² = b²+ c² − 2bc cos α

a² = 45²+ 60² − (2 x 45 x 60) cos 30

a² = 2025 + 3600 - 5400 cos 30

a² = 5625 - 5400 x 0.866

a² = 948

a = 31

The force is 31 N