Leaning ladder against a wall: A ladder makes a 60° angle with the horizontal ground, and its foot is 4.6 m away from the wall. Find the length of the ladder.

Introduction / Context:
A ladder against a wall forms a right triangle with the ground (adjacent) and wall (opposite). The angle with ground and the horizontal distance to the wall are known; find the hypotenuse (ladder length).

Given Data / Assumptions:

• Angle with ground = 60°.
• Adjacency (foot to wall) = 4.6 m.
• Ladder is straight; wall and ground are perpendicular.

Concept / Approach:
Use cos θ = adjacent / hypotenuse → hypotenuse = adjacent / cos θ.

Step-by-Step Solution:

Verification / Alternative check:
Compute vertical reach: L * sin 60° = 9.2 * (√3/2) ≈ 7.97 m; Pythagoras with 4.6 m confirms hypotenuse ≈ 9.2 m.

Why Other Options Are Wrong:
2.3 and 4.6 m are too short; 7.8 m corresponds to cos near 0.59, not 0.5.

Common Pitfalls:
Using tan instead of cos; mixing degrees with radians; rounding too early on √3 or cos values.

Final Answer:
9.2 m