A painter wants to lean a 30-foot ladder against a wall. Safety guidelines recommend that the distance between the base of the ladder and the wall should be 1/4 of the length of the ladder. To the nearest degree, what acute angle should the ladder make with the ground? Enter only the number
To determine the acute angle that the ladder should make with the ground, we can use trigonometric functions.
Based on the safety guideline, the distance between the base of the ladder and the wall should be 1/4 of the length of the ladder.
Given that the length of the ladder is 30 feet, we can calculate the distance between the base and the wall as follows:
Distance = (1/4) * 30 feet = 7.5 feet
Now, using the trigonometric function tangent (tan), we can find the angle:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the wall, which is 7.5 feet, and the adjacent side is the length of the ladder, which is 30 feet.
tan(angle) = 7.5/30
Simplifying this, we get:
tan(angle) = 1/4
To find the angle, we take the inverse tangent (arctan) of both sides:
angle = arctan(1/4) ≈ 14.04 degrees
Therefore, to the nearest degree, the acute angle that the ladder should make with the ground is 14 degrees.
To find the angle, we can use trigonometry. Let's assume that the base of the ladder is x feet away from the wall. According to the safety guidelines, the distance between the base of the ladder and the wall should be 1/4 of the length of the ladder, which is 30 feet in this case.
So we have:
x = 1/4 * 30
x = 7.5 feet
Now, we can use the tangent function to find the angle. The tangent of an angle is equal to the ratio of the opposite side (the height of the wall) to the adjacent side (the distance from the base of the ladder to the wall).
tan(angle) = opposite/adjacent
tan(angle) = x/30
tan(angle) = 7.5/30
Using a calculator, we can find the inverse tangent (tan^(-1)) of 7.5/30 to get the angle:
angle = tan^(-1)(7.5/30)
angle ≈ 14.48 degrees
Hence, the acute angle that the ladder should make with the ground, to the nearest degree, is approximately 14 degrees.
The length of the ladder does not matter. We are told that
cos x = 1/4
x = 75.52°