Question

what is the value of $\sin(\angle n)$?
$\frac{12}{13}$
$\frac{5}{13}$
$\frac{12}{5}$
$\frac{5}{12}$

Explanation:

Step1: Recall the sine formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify the sides relative to $\angle N$

For $\angle N$, the opposite side is $PQ = 5$ and the hypotenuse is $NP=13$.

Step3: Calculate $\sin(\angle N)$

Using the formula $\sin(\angle N)=\frac{PQ}{NP}$, substituting $PQ = 5$ and $NP = 13$, we get $\sin(\angle N)=\frac{5}{13}$.

Answer:

$\frac{5}{13}$