A ladder 12 m in length rests against a wall. The foot of the ladder is 3 m from the wall. What is the measure of the angle the ladder forms with the floor?

Use cosine (let x = angle):

cos (x) = 3/12
Solve for x.

To find the measure of the angle the ladder forms with the floor, we can use trigonometry. Specifically, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this scenario, the ladder is the hypotenuse of a right triangle, and the side opposite the angle is the distance between the foot of the ladder and the wall (3 m). The side adjacent to the angle is the height of the wall where the ladder rests.

Let's call the angle we're trying to find θ.

Using the tangent function, we have:

tan(θ) = opposite/adjacent

tan(θ) = 3m/h, where h is the height of the wall.

To solve for θ, we need to isolate it. By taking the inverse tangent (arctan) of both sides of the equation, we obtain:

θ = arctan(3m/h)

Now, in order to find the value of θ, we need to know the height of the wall. If the height is given in the problem statement, we can substitute it into the equation and calculate the angle. Otherwise, if the height is not provided, we can't determine the actual measure of the angle.