Question

three forces of 114 lbs, 120 lbs, and 210 lbs are in equilibrium. find the measure of the angle between the 114 lb force and the 120 lb force

Answer 1

Answer: θ = 97.8°

Step-by-step explanation: Three forces in equilibrium form a triangle. To determine the angle, we can use Law of Cosines, which relates the side of a triangle to the cosine of one of its angles.

The relationship is given as

`a^(2)=b^(2)+c^(2)-2bccos\theta`

For the three forces, cosine law is

`210^(2)=114^(2)+120^(2)-2(114)(120)cos\theta`

`44100=12996+14400-27360cos\theta`

`27360cos\theta=-3708`

`cos\theta=-0.1355`

`\theta = cos^(-1)(-0.1355)`

`\theta=` 97.8°

The angle between forces 114lb and 120lb is 97.8°