Discussion
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Answer: A
The ladder is the hypotenuse and the ground gap is the side adjacent to the 60° angle, so cosine is the ratio to use.
\[ \cos 60^{\circ} = \frac{\text{distance from wall}}{\text{ladder length}} \]
\[ \frac{1}{2} = \frac{4.6}{L} \quad\Longrightarrow\quad L = 2 \times 4.6 = 9.2 \text{ m} \]
Since \( \cos 60^{\circ} = \tfrac{1}{2} \), the ladder is always exactly twice the foot distance here. Reaching for \( \tan \) or \( \sin \) instead gives \( 4.6\sqrt{3} \) - the wall height, not the ladder.
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