Question

solving for measures of right triangles
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: Calculate angle L

Sum of triangle angles is $180^\circ$.
$\angle L = 180^\circ - 90^\circ - 20^\circ = 70^\circ$

Step2: Identify trigonometric ratio

For $\angle M$, $LN$ is opposite, $NM$ is adjacent.
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, so use tangent.

Step3: Solve for length NM

Rearrange $\tan(20^\circ) = \frac{21}{NM}$ to isolate $NM$.
$NM = \frac{21}{\tan(20^\circ)}$
Calculate $\tan(20^\circ) \approx 0.3640$, so $NM \approx \frac{21}{0.3640} \approx 57.7$

Answer:

The measure of angle L is $70^\circ$
The trigonometric ratio that uses $\angle M$ and $LN$ to solve for $NM$ is tangent
The length of $NM$, to the nearest tenth, is approximately $57.7$