Final answer:
To find the angle the resultant force makes with the 14lb force, use the arctan of the ratio of the two force magnitudes. The angle is approximately 19.65 degrees.
Step-by-step explanation:
The question involves finding the angle that the resultant force makes with one of the component forces when two forces act at right angles to each other. This is a typical physics problem involving vector addition and trigonometry. To find the angle, we can use trigonometric functions, specifically the tangent function, since we know the magnitudes of the two forces. The tangent of the angle θ is equal to the opposite side (the force of 5lb) over the adjacent side (the force of 14lb). Applying arctangent to solve for θ, we get:
- tan(θ) = 5lb / 14lb
- θ = arctan(5lb / 14lb)
- θ = arctan(0.357)
- θ ≈ 19.65 degrees
The resultant force makes an angle of approximately 19.65 degrees with the 14lb force. It's important to use a calculator to find the arctan (inverse tangent) value, which will give the angle in degrees.