Question

opposite side/hypotenuse =

Explanation:

Step1: Apply Pythagorean theorem

$$\begin{align*} AB^{2}&=BC^{2}+AC^{2}\\ AB^{2}&=(\sqrt{3})^{2}+(\sqrt{13})^{2}\\ AB^{2}&=3 + 13\\ AB^{2}&=16\\ AB& = 4 \end{align*}$$

Step2: Calculate the ratio

The opposite side to angle \(A\) is \(BC=\sqrt{3}\), and the hypotenuse \(AB = 4\). So \(\frac{\text{OPPOSITE SIDE}}{\text{HYPOTENUSE}}=\frac{BC}{AB}\)

Answer:

\(\frac{\sqrt{3}}{4}\)