Discussion
A ladder leaning against a vertical wall makes an angle of \( 45^{\circ} \) with the level ground. The foot of the ladder is 3 m from the wall. Find the length of the ladder.
Answer: A
The ladder is the hypotenuse and the 3 m is adjacent to the \( 45^{\circ} \) angle, so cosine relates them.
\[ \cos 45^{\circ} = \frac{3}{L} \quad\Longrightarrow\quad \frac{1}{\sqrt{2}} = \frac{3}{L} \]
\[ L = 3\sqrt{2} = 3 \times 1.414 = 4.243 \approx 4.23 \text{ m} \]
At \( 45^{\circ} \) the ladder reaches 3 m up the wall as well, so it is the diagonal of a 3 m square - hence the factor \( \sqrt{2} \).
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