Final answer:
The 12-m ladder must make an angle of approximately 76 degrees with the ground to meet the national fire safety code that dictates the ladder's placement at a quarter of its length from the wall.
Step-by-step explanation:
The question at hand involves determining the angle a ladder makes with the ground when placed according to the national fire safety code, which requires that the distance from the foot of the ladder to the wall be one quarter of the ladder's length. Given a 12-m ladder, we can use the tangent function to find the angle, since the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the opposite side is the height the ladder reaches on the wall, and the adjacent side is the distance from the foot of the ladder to the wall.
To calculate the angle, we set up the equation: tan(θ) = (length of the ladder) / (distance from the foot of the ladder to the wall). Substituting the given values, we have tan(θ) = 12 / (12/4), which simplifies to tan(θ) = 4. Using inverse tangent (arctan), we find that θ = arctan(4). Performing this calculation yields an angle of approximately 76 degrees. Therefore, a 12-m ladder must make an angle of about 76 degrees with the ground when placed according to the firefighter's guidelines.