Answer:
∠ L ≈ 21.6°
Step-by-step explanation:
Using the Sine rule in the triangle
[tex]\frac{MN}{sinL}[/tex] = [tex]\frac{LM}{sinN}[/tex] , that is
[tex]\frac{34}{sinL}[/tex] = [tex]\frac{42}{sin27}[/tex] ( cross- multiply )
42 × sinL = 34 × sin27° ( divide both sides by 42 )
sinL = [tex]\frac{34sin27}{42}[/tex] , then
∠ L = [tex]sin^{-1}[/tex] ( [tex]\frac{34sin27}{42}[/tex] ) ≈ 21.6° ( to the nearest tenth )
