A roofer must set up a 40-foot ladder against the side of a house. He sets the ladder so that the distance from the base of the ladder to the wall is 1/5 of the length of the ladder. To the nearest degree, what acute angle does the ladder make with the ground? (Hint: Sketch the problem before solving.)

cos theta = .2

0.999 To solve this problem, we can use trigonometry.

Let's first sketch the problem. We have a right triangle, where the ladder represents the hypotenuse, the distance from the base of the ladder to the wall represents one of the legs, and the ground represents the other leg.

Based on the information given, the length of the ladder is 40 feet, and the distance from the base of the ladder to the wall is 1/5 of the length of the ladder. So, this distance can be calculated as:

1/5 * 40 = 8 feet

Now, we have a right triangle with a leg of 8 feet and the hypotenuse (ladder) of 40 feet. We need to find the acute angle that the ladder makes with the ground.

To find this angle, we can use the sine function since we have the opposite and hypotenuse sides.

sin(angle) = opposite/hypotenuse

sin(angle) = 8/40

Or, we can simplify it further:

sin(angle) = 1/5

To find the angle, we can take the inverse sine (sin^-1) of both sides:

angle = sin^-1(1/5)

Using a calculator, we find:

angle ≈ 11.54 degrees

Therefore, to the nearest degree, the acute angle that the ladder makes with the ground is approximately 12 degrees.