Explanation

Given:

Angle of elevation (θ) = 60°

Distance of the foot of the ladder from the wall (x) = 4.6 m

We can use the tangent function to relate the angle, distance, and length of the ladder (hypotenuse):

tan(θ) = opposite side (height) / adjacent side (distance)

tan(60°) = height / 4.6

To find the height, we can multiply both sides by 4.6:

height = 4.6 × tan(60°)

height ≈ 4.6 × 1.732 (using a calculator)

height ≈ 7.96 m

Now, we can use the Pythagorean theorem to find the length of the ladder (hypotenuse):

length² = height² + distance²

length² = 7.96² + 4.6²

length² = 63.37 + 21.16

length² = 84.53

length ≈ √84.53

length ≈ 9.2 m

So, the length of the ladder is approximately 9.2 meters.