In triangle ABC, the angle between sides AB and BC is 30 degrees. how will the area of triangle ABC

In triangle ABC, the angle between sides AB and BC is 30 degrees. how will the area of triangle ABC change if the angle between sides AB and BC increases by 120 degrees?

Since the lengths of the sides AB = A1B1, BC = B1C1, we denote AB = A1B1 = X cm, BC = B1C1 = Y cm.

Determine the area of the triangle ABC.

Savs = AB * BC * Sin30 = X * Y * (1/2). = X * Y / 2 cm2.

Let’s define the area of the triangle A1B1C1.

Sa1bc1 = A1B1 * B1C1 * Sin120 = X * Y * √3 / 2 cm2.

Let’s find the ratio of the areas of the triangle A1B1C1 and ABC.

Sa1vs1 / Saavs = (X * Y * √3 / 2) / (X * Y / 2) = √3.

Answer: The area of the triangle will increase by √3 times.