High School

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A force of magnitude 112 lb and one of 84 lb are applied to an object at the same point. The resultant force has a magnitude of 162 lb.

Determine the angle between the two forces.

Answer :

The angle between the 112 lb force and the 162 lb resultant force is approximately 95.2 degrees to the nearest tenth of a degree.

To find the angle between the forces of 112 lb and the resultant force of 162 lb, we will use the Law of Cosines. The Law of Cosines states that, for any triangle with sides of lengths a, b, and c, and an angle C between sides a and b:

c² = a² + b² - 2ab * cos(C)

In this problem, we have a triangle with sides a = 112 lb, b = 84 lb, and c = 162 lb. We want to find angle C, which is the angle between the 112 lb and 162 lb forces.

First, plug in the values into the Law of Cosines formula:

162² = 112² + 84² - 2(112)(84) * cos(C)

Now, we will solve for cos(C):

cos(C) = (162² - 112² - 84²) / (2 * 112 * 84)

Calculate the values:

cos(C) ≈ -0.0908

To find angle C, take the inverse cosine (arccos) of the value:

C = arccos(-0.0908)

C ≈ 95.2 degrees

So, the angle between the 112 lb force and the 162 lb resultant force is approximately 95.2 degrees to the nearest tenth of a degree.

The complete question is:

A force of magnitude 112 lb and one of 84 lb are applied to an object at the same point and the resultant force has a magnitude of 162 lb. Find to the nearest tenth of a degree the angle made by the resultant force with the force of 112 lb.

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