By first calculating the size of angle LMN, calculate the area of triangle MNL.
You must show all your working.
ML is 4.8cm
LN is 7.2 cm
angle N is 38 degrees

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  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

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