In triangle ABC AB = BC = 12 cm, angle A = angle C = 75 degrees. Find the area ABC.

1. Find ∠В.

The sum of all the angles of a triangle is 180 °. Means,

∠А + ∠С + ∠В = 180 °;

∠В = 180 ° – ∠А – ∠С;

∠В = 180 ° – 75 ° – 75 °;

∠В = 30 °.

2. Find the area of the triangle ABC, knowing the two sides and the angle between them, by the formula:

S △ ABC = 1/2 * AB * AC * sin∠B;

S △ ABC = 1/2 * 12 * 12 * sin 30 °;

S △ ABC = 1/2 * 12 * 12 * 1/2;

S △ ABC = (1 * 12 * 12 * 1) / (2 * 2);

S △ ABC = 144/4;

S △ ABC = 36 cm2.

Answer: S △ ABC = 36 cm2.