Question

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

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle M = 20^{\circ}$, the hypotenuse is $ML = 8$, the side opposite to $\angle M$ is $LN$ and the side adjacent to $\angle M$ is $MN$. For $\angle L=70^{\circ}$, the side opposite to $\angle L$ is $MN$ and the side adjacent to $\angle L$ is $LN$.

Step2: Analyze $\sin(20^{\circ})$

$\sin(20^{\circ})=\frac{LN}{8}$ since for $\angle M = 20^{\circ}$, the opposite side to $\angle M$ is $LN$ and the hypotenuse is $8$.

Step3: Analyze $\cos(70^{\circ})$

Since $\angle M = 20^{\circ}$ and $\angle L=70^{\circ}$ in a right - triangle, and $\cos(70^{\circ})=\sin(20^{\circ})$. Also, $\cos(70^{\circ})=\frac{LN}{8}$ because for $\angle L = 70^{\circ}$, the adjacent side to $\angle L$ is $LN$ and the hypotenuse is $8$.

Answer:

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