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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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

Final answer:

To calculate the area of triangle MNL, first calculate the size of angle LMN using the Cosine Rule. Then use that angle and the known side lengths in the formula for the area of a triangle (Area = 0.5 * a * b * sin(C)) to find the area.

Explanation:

To solve this, you need to first calculate the size of angle LMN. This can be done using the Cosine Rule, which states that cos(C) = (a² + b² - c²) / 2ab, where a and b are the sides enclosing angle C. Here, angle C would be LMN, and sides a and b would be ML and LN.

Applying the values from your question, the cosine of LMN would be cos(LMN) = (4.8² + 7.2² - 38²) / (2 * 4.8 * 7.2). After calculating the cosine of the angle, you can find the angle itself using the inverse cosine function, or arccos.

Once you have the size of angle LMN, you can calculate the area of the triangle using the formula Area = 0.5 * a * b * sin(C), where a and b are sides of the triangle and C is the included angle. So, the area of triangle MNL would be Area = 0.5 * ML * LN * sin(LMN).

Learn more about Triangle Area Calculation here:

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