Question

observa el $\triangle lmn$.
¿cuál es el valor de $\sen l$?
\bigcirc a. 1
\bigcirc b. $\frac{1}{2}$
\bigcirc c. $\frac{\sqrt{3}}{2}$

Explanation:

Step1: Recall sine definition

$\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle L$

Opposite side to $\angle L$ is $NM$, hypotenuse $LN=1$.

Step3: Calculate length of $NM$

In 30-60-90 triangle, side opposite $30^\circ$ is $\frac{1}{2}$ hypotenuse: $NM = \frac{1}{2} \times 1 = \frac{1}{2}$

Step4: Compute $\sin L$

$\sin L = \frac{NM}{LN} = \frac{\frac{1}{2}}{1} = \frac{1}{2}$

Answer:

B. $\frac{1}{2}$