Question

express sin n as a fraction in simplest terms.

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $N$, the side opposite to angle $N$ is $PO$ and the hypotenuse is $PN$.

Step2: Find the length of the opposite side

First, use the Pythagorean theorem to find the length of $PO$. Let $PO = x$. Then $x=\sqrt{PN^{2}-NO^{2}}=\sqrt{50^{2}-48^{2}}=\sqrt{(50 + 48)(50 - 48)}=\sqrt{98\times2}=\sqrt{196}=14$.

Step3: Calculate $\sin N$

$\sin N=\frac{PO}{PN}$. Since $PO = 14$ and $PN = 50$, then $\sin N=\frac{14}{50}=\frac{7}{25}$.

Answer:

$\frac{7}{25}$