Two forces, a horizontal force of 45 lb and another of 54 lb, act on the same object. The angle between these forces is 25°. Find the magnitude (in lb) and direction angle from the positive x-axis of the resultant force that acts on the object. (Round your answers to two decimal places.)

The magnitude is 96.67 lb and the direction angle from the positive x-axis is 13.65º.

Step-by-step explanation:

To find the effect of combining the two forces, add their representative vectors.

First, express each vector in component form or in terms of the standard unit vectors. For this purpose, it is easiest if we align one of the vectors with the positive x-axis. The horizontal vector, then, has initial point (0, 0) and terminal point (45, 0). It can be expressed as

The second vector has magnitude 54 and makes an angle of 25° with the first, so we can express it as

Then, the sum of the vectors, or resultant vector, is

The magnitude is

The angle made by and the positive x-axis has

which means the resultant force has an angle of 13.65° above the horizontal axis.

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