A box is on a 10 degree incline with 180 pounds of force against the box. What is the weight of the box?

well, you know it's gotta be either sine or cosine of the angle.

0° means the whole weight, so it looks like 180cos10°

To find the weight of the box, we need to understand the forces acting on it.

The force against the box can be broken down into two components: the force perpendicular to the incline (normal force) and the force parallel to the incline (component of the force due to gravity).

The weight of an object is the force due to gravity acting on it. It can be calculated using the formula:

Weight = mass × gravitational acceleration

To find the weight, we need to determine the mass of the box. Since we are given the force in pounds, we can convert it to mass using the conversion factor:

1 mass unit = 1 lb / gravitational acceleration

The gravitational acceleration is approximately 32.2 feet per second squared.

To use this formula on an incline, we need to consider the component of the force due to gravity acting parallel to the incline. This component can be calculated by multiplying the weight of the object by the sine of the angle of the incline.

Force parallel to the incline = Weight × sin(angle of incline)

In this case, the angle of incline is given as 10 degrees and the force against the box is 180 pounds.

So, let's calculate the weight of the box step by step:

1. Convert the force from pounds to mass:
Mass = Force / gravitational acceleration
Mass = 180 lb / 32.2 ft/s^2

2. Calculate the weight of the box:
Weight = Mass × gravitational acceleration

3. Calculate the force parallel to the incline:
Force parallel to incline = Weight × sin(angle of incline)

By following these steps, you can find the weight of the box on a 10-degree incline with 180 pounds of force against it.