What is the area of triangle ABC if the sides AB and BC are 4 and 6 cm, respectively

What is the area of triangle ABC if the sides AB and BC are 4 and 6 cm, respectively, and the outer angle at the vertex B is 150 degrees?

1) Property of the outer corner of a triangle: the outer corner of a triangle is equal to the sum of two inner angles that are not adjacent to it. ∠1 = 180º – ∠ABC. ∠1 is the outer corner of the triangle. On condition, it is equal to 150 degrees. Substitute 150 for ∠1. We get: 150 = 180 – ∠ABC. Let us express ∠ABC by moving the unknown to the left and the free term to the right. We get: ∠ABC = 180 – 150; ∠ABC = 30 degrees.

2) Area of triangle: S = 1/2 * AB * BC * sin (∠ABC) = 1/2 * AB * BC * sin (30) = 1/2 * 4 * 6 * sin (30) = 1/2 * 4 * 6 * 1/2 = 6 cm ^ 2.