Answer:
m(∠LMN) = 67.44°
Area of ΔMNL = 16.66 square units
Step-by-step explanation:
By applying Sine rule in the ΔLMN,
[tex]\frac{\text{Sin}M}{\text{NL}}=\frac{\text{Sin}N}{\text{ML}}[/tex]
[tex]\frac{\text{Sin}M}{7.2}}=\frac{\text{Sin}38}{\text{4.8}}[/tex]
SinM = [tex]\frac{\text{Sin}38\times 7.2}{4.8}[/tex]
SinM = 0.9235
M = [tex]\text{Sin^{-1}}(0.9235)[/tex][tex]\text{Sin}^{-1} (0.9235)[/tex]
M = 67.44°
m(∠M) + m(∠N) + m(∠L) = 180°
67.44 + 38 + m(∠L) = 180°
m(∠L) = 180 - 105.44
m(∠L) = 74.56°
Area of ΔMNL = [tex]\frac{1}{2}(\text{ML})(\text{NL})\text{Sin}(74.56)[/tex]
= [tex]\frac{1}{2}(4.8)(7.2)(0.96391)[/tex]
= 16.66 square units