A ladder leans against a vertical wall, making a 60° angle with the ground. The foot of the ladder is 12.4 m from the wall. Find the length of the ladder (in metres).

Introduction / Context:
Ladders against walls are right-triangle problems. The ladder is the hypotenuse, the distance of the foot from the wall is the adjacent side, and the angle with ground gives a direct cosine relation.

Given Data / Assumptions:

• Angle with ground θ = 60°.
• Adjacent side (base) = 12.4 m.
• Right triangle with the wall.

Concept / Approach:
cos θ = adjacent / hypotenuse ⇒ hypotenuse = adjacent / cos θ.

Step-by-Step Solution:

Verification / Alternative check:
Using sin 60° for height: height = 24.8 * (√3/2) ≈ 21.47 m; then tan 60° = height/12.4 ≈ 21.47/12.4 ≈ 1.73 ≈ √3; consistent.

Why Other Options Are Wrong:
12.4 m is just the base; 14.8 and 22.8 m contradict cos 60°; 6.2 m halves the base incorrectly.

Common Pitfalls:
Confusing which side is adjacent/opposite; using tan instead of cos for this configuration.

Final Answer:
24.8 m