9514 1404 393
Answer:
16.66 cm² or 8.49 cm²
Step-by-step explanation:
The law of sines is useful for this.
sin(N)/LM = sin(M)/LN
M = arcsin(sin(N)×LN/LM) = arcsin(sin(38°)×7.2/4.8)
M =67.44° or 112.56°
Angle L is the remaining angle, so will have one of two measures:
L1 = 180° -38° -67.44° = 74.56°
The area of that triangle is ...
A = (1/2)LM×LN×sin(74.56°) ≈ 16.66 . . . . cm²
or ...
L2 = 180° -38° -112.56° = 29.44°
The area of that triangle is ...
A = (1/2)LM×LN×sin(29.44°) ≈ 8.49 . . . . cm²
