find the angle between the two forces.

Question

two forces of 130 and 150 pounds yield a resultant force of 170 pounds. Find, to the nearest tenth of a degree, the angle between the original two forces.

Answer 1

two forces of 130 and 150 pounds yield a resultant force of 170 pounds. Find, to the nearest tenth of a degree, the angle between the original two forces.

Here is a Force diagram of the two forces, b = 130 lb, c = 150 lb with their resultant force, a = 170 lb.

 

We use the cosine rule here.

a^2 = b^2 + c^2 – 2bc.cos(A)

cos(A) = (b^2 + c^2 – a^2) / (2bc)

cos(A) = (130^2 + 150^2 – 170^2) / (2*130*15))

cos(A) = (16,900 + 22,500 - 28,900) / (39,000)

cos(A) = 500 / 39,000 = 0.0128205

A = 89.265418° = 89° 15’ 55.45”

Angle between the two original forces is: 89.3°