Question

use the diagram to complete the statements. the measure of angle l is . the trigonometric ratio that uses ∠m and ln to solve for nm is . the length of nm, to the nearest tenth, is approximately .

Explanation:

Step1: Identify trig - ratio

We know $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = \angle M = 20^{\circ}$, opposite side to $\angle M$ is $LN = 21$ and adjacent side is $NM$. So $\tan M=\tan(20^{\circ})=\frac{LN}{NM}$.

Step2: Solve for $NM$

$NM=\frac{LN}{\tan M}=\frac{21}{\tan(20^{\circ})}$. Using a calculator, $\tan(20^{\circ})\approx0.364$, so $NM=\frac{21}{0.364}\approx57.7$.

Answer:

The measure of angle $L$ is $70^{\circ}$ (since in right - triangle $LMN$, $\angle L = 90^{\circ}-\angle M=90 - 20=70^{\circ}$), the trigonometric ratio that uses $\angle M$ and $LN$ to solve for $NM$ is $\tan$, and the length of $NM$, to the nearest tenth, is approximately $57.7$.