Question

what are the correct trigonometric ratios that could be used to determine the length of ln? check all that apply. sin(20°)=ln/8 cos(70°)=8/ln tan(70°)=ln/mn sin(20°)=8/ln cos(70°)=ln/8

Explanation:

Step1: Recall trig - ratio definitions

In right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle M = 20^{\circ}$, $\sin(20^{\circ})=\frac{LN}{LM}=\frac{LN}{8}$. Also, $\cos(70^{\circ})=\frac{LN}{LM}=\frac{LN}{8}$ since $70^{\circ}$ and $20^{\circ}$ are complementary.

Answer:

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