The angle of elevation of a ladder leaning against a wall is 60° and the foot…

Concept: In a right triangle, if θ is the angle a slanted line (such as a ladder) makes with the ground, then cos θ = (adjacent side) / (hypotenuse), where the adjacent side is the horizontal distance from the wall and the hypotenuse is the length of the ladder itself.

1. Let the length of the ladder be L (the hypotenuse) and the distance of the foot of the ladder from the wall be 4.6 m (the side adjacent to the 60° angle of elevation).

2. Apply the cosine ratio: cos(60°) = Adjacent / Hypotenuse = 4.6 / L.

3. Since cos(60°) = 1/2, this gives 1/2 = 4.6 / L.

4. Solving for L: L = 2 × 4.6 = 9.2 m.

Cross-check: With L = 9.2 m, the adjacent side works out to L × cos(60°) = 9.2 × 0.5 = 4.6 m, matching the given distance, and the hypotenuse (9.2 m) is correctly longer than the adjacent side (4.6 m), confirming the ladder length is 9.2 m.