Question

find the value of \\( \sin l \\) rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall the sine formula

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

Step2: Identify the sides relative to angle $L$

For angle $L$, the opposite side is $MN = 10$, and the hypotenuse is $LN=26$.

Step3: Calculate $\sin L$

$\sin L=\frac{MN}{LN}=\frac{10}{26}=\frac{5}{13}\approx0.38$ (rounded to the nearest hundredth).

Answer:

$\frac{5}{13}$