Question

PLEASE!!!!Solving for Measures of Right Triangles:

Answer 1

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

Answer 2

We know, by angle-sum property, that ∠L + ∠M+ ∠N = 180°

∠L + 20°+ 90° = 180°

∠L = 180° - 110° = 70°

For angle ∠M, side LN is opposite side and side NM is adjacent side.

So, the trigonometric ratio which uses these sides is tangent.

In Δ LMN,

$tan 20 = \frac{21}{NM}$

0.364 NM = 21

NM = 21/0.364

NM = 57.7 rounded to nearest tenth.