Discussion
A 15-meter long ladder reached a window, x meter high from the ground when placed against a wall at a distance of y meter. If the angle between ladder and ground is 30°, then about x and y which of the following is true?
Answer: A
The answer is x = 7.5 metre and y = \(15\sqrt{3}/2\) metre.
The ladder is the hypotenuse, 15 m, making 30° with the ground. The height reached is the side opposite that angle and the distance from the wall the side adjacent to it:
\[ \begin{aligned} x &= 15 \sin 30^\circ = 7.5\ \text{m} \\ y &= 15 \cos 30^\circ = \frac{15\sqrt{3}}{2}\ \text{m} \end{aligned} \]
Option B swaps the two, which would be right only for a 60° angle with the ground. The values with \(\sqrt{2}\) belong to a 45° angle.
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