Question

The resultant of two forces acting at a point at right angles to each other is 40 pounds. If the horizontal force is 30 pounds, what angle does it make with the resultant?

A. 37°

B. 41°

C. 49°

D. 53°

Answer 1

To find the angle between the horizontal force and the resultant force, we use the tangent function and the arctan function. The angle is approximately 37°.

Step-by-step explanation:

To find the angle between the horizontal force and the resultant force, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the vertical component of the resultant force, which is the square root of (40^2 - 30^2) pounds. The adjacent side is the horizontal force, which is 30 pounds. Therefore, the angle can be found using the arctan function: angle = arctan(opp/adj) = arctan((sqrt(40^2 - 30^2))/30).

Calculating this value, we get an angle of approximately 37°. Therefore, the correct answer is A. 37°.