Question

(b)
\\( \frac { \text { opposite side } } { \text { adjacent side } } = \\)
\\( \frac { \text { opposite side } } { \text { hypotenuse } } = \\)
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Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 2\), \(b=\sqrt{5}\).
\(AB=\sqrt{2^{2}+(\sqrt{5})^{2}}=\sqrt{4 + 5}=\sqrt{9}=3\)

Step2: Calculate \(\frac{\text{opposite side}}{\text{adjacent side}}\)

Assume we are considering angle \(A\), the opposite side to angle \(A\) is \(BC = 2\), and the adjacent side to angle \(A\) is \(AC=\sqrt{5}\). So \(\frac{\text{opposite side}}{\text{adjacent side}}=\frac{2}{\sqrt{5}}=\frac{2\sqrt{5}}{5}\)

Step3: Calculate \(\frac{\text{opposite side}}{\text{hypotenuse}}\)

The opposite side to angle \(A\) is \(BC = 2\), and the hypotenuse \(AB = 3\). So \(\frac{\text{opposite side}}{\text{hypotenuse}}=\frac{2}{3}\)

Answer:

\(\frac{2\sqrt{5}}{5}\), \(\frac{2}{3}\)