Discussion
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:
Answer: C
The ladder is the hypotenuse; the 12.4 m ground gap is adjacent to the \( 60^{\circ} \) elevation, so cosine relates them.
\[ \cos 60^{\circ} = \frac{12.4}{L} \quad\Longrightarrow\quad \frac{1}{2} = \frac{12.4}{L} \]
\[ L = 2 \times 12.4 = 24.8 \text{ m} \]
Because \( \cos 60^{\circ} = \tfrac{1}{2} \), the ladder is always exactly twice the foot distance at this angle. Using \( \tan \) instead returns \( 12.4\sqrt{3} = 21.5 \) m, which is the height reached up the wall.
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