Question

what are the correct trigonometric ratios that could be used to determine the length of ln? choose two correct answers. sin(20°)=8/ln cos(70°)=8/ln sin(20°)=ln/8

Explanation:

Step1: Recall trigonometric - ratio definitions

In right - triangle $\triangle LMN$ with right - angle at $N$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Analyze angles and sides

The angle $\angle M = 20^{\circ}$ and the side $LM = 8$. The side opposite $\angle M$ is $LN$. So, $\sin(20^{\circ})=\frac{LN}{LM}=\frac{LN}{8}$, which can be rewritten as $LN = 8\sin(20^{\circ})$. Also, the angle $\angle L=70^{\circ}$, and the side adjacent to $\angle L$ is $LN$ and the hypotenuse is $LM = 8$. So, $\cos(70^{\circ})=\frac{LN}{LM}=\frac{LN}{8}$.

Answer:

$\sin(20^{\circ})=\frac{LN}{8}$, $\cos(70^{\circ})=\frac{LN}{8}$