Final answer:
By using the cosine function with the given angle of 50 degrees and the known distance from the wall (6m), we find that the length of the ladder is approximately 9.64 meters.
Step-by-step explanation:
To solve the problem of determining the length of the ladder, we need to apply trigonometric principles. Specifically, we need to use the cosine function, which relates the angle a ladder makes with the ground to its length and the distance from the wall.
Step-by-Step Solution for the Ladder's Length:
Let the length of the ladder be L.
The distance from the base of the ladder to the wall is given as 6m.
The angle made by the ladder with the ground is 50 degrees.
Using the cosine function: cos(50°) = adjacent/hypotenuse, where the adjacent side is the distance from the wall (6m) and the hypotenuse is L.
Rearrange the equation to solve for L: L = 6m / cos(50°).
Calculate the length using a calculator: L ≈ 9.64m.
The ladder is approximately 9.64 meters long.