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: D
The ladder is the hypotenuse and the 4.6 m ground gap is adjacent to the \( 60^{\circ} \) elevation, so cosine is the ratio.
\[ \cos 60^{\circ} = \frac{4.6}{L} \quad\Longrightarrow\quad \frac{1}{2} = \frac{4.6}{L} \]
\[ L = 2 \times 4.6 = 9.2 \text{ m} \]
Since \( \cos 60^{\circ} = \tfrac{1}{2} \), the ladder is exactly twice the foot distance. Using tangent instead returns \( 4.6\sqrt{3} = 7.97 \) m, which is the height reached on the wall - hence the 7.8 m distractor.
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