To find the length of the ladder, we can use trigonometry. The situation forms a right triangle where the ladder is the hypotenuse, the distance from the wall to the base of the ladder is one side, and the height at which the ladder touches the wall is the other side.

Given: Angle of elevation (θ) = 60 degrees Distance from the wall to the base of the ladder (adjacent side) = 4.6 meters

We want to find the length of the ladder (hypotenuse).

Using the trigonometric relationship for a right triangle:

cos(θ) = adjacent side / hypotenuse

cos(60 degrees) = 4.6 / hypotenuse

Now, calculate the value of cos(60 degrees):

cos(60 degrees) = 0.5

Now, rearrange the formula to solve for the hypotenuse (length of the ladder):

hypotenuse = adjacent side / cos(60 degrees) hypotenuse = 4.6 / 0.5

hypotenuse = 9.2 meters

So, the length of the ladder is 9.2 meters. The answer is 9.2 meters.