Question

PLEASE!!!!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 .

Answer 1

Angle L = 70
The ratio is = tangent
The length of NM is = 57.7

Answer 2

The measure of angle L is $70^\circ$, the trigonometric ratio that uses $\rm \angle M$ and LN to solve for NM is a tangent and the length of NM is 57.70 units.

Given :

• Triangle LMN.

• $\rm \angle M = 20^\circ$
• $\rm \angle N = 90^\circ$

• Length of NL = 21 units.

Solution :

We know that the sum of all three interior angles of a triangle is $180^\circ$.

$\rm \angle M +\angle N + \angle L = 180^\circ$

$\rm 20^\circ + 90^\circ + \angle L = 180^\circ$

$\rm \angle L = 180^\circ - 110^\circ$

$\rm \angle L = 70^\circ$

It is given that the triangle LMN is a right angle triangle so NM is perpendicular, LM is hypotenuse and LN is base.

From trignometry function we know that the formula of $\rm tan\theta$ is given by:

$\rm tan \theta = \dfrac{Perpendicular}{Base}$

$\rm tan (L) = \dfrac{ MN }{21}$

$\rm 2.7474\times 21 = MN$

MN = 57.70 units

From trignometry function we know that the formula of $\rm sin\theta$ is given by:

$\rm sin \theta = \dfrac{Perpendicular}{Hypotenuse}$

$\rm sin(70^\circ) = \dfrac{57.70}{LM}$

LM = 61.40 units

The trigonometric ratio that uses $\rm \angle M$ and LN to solve for NM is a tangent.

For more information, refer the link given below

https://brainly.com/question/19731462