What is S (triangle ABC) if AB = 4cm. ВС = 6cm outside angle at the apex В = 150 degrees.

A triangle is three points on a plane that do not lie on one straight line, connected by segments. In this case, the points are the vertices of the triangle, and the segments are its sides.

To calculate the area of ​​a triangle, we will use the formula for the area behind two sides and the angle between them:

S = 1/2 * a * b * sin α, where:

S is the area of ​​the triangle;

a, b – sides of the triangle;

α is the angle between them.

To do this, we need to find the value of the angle ∠B.

Since the outer angle at the vertex B is equal to 150º, and the sum of the outer and inner angles of the triangle at one vertex is equal to

180º, then:

∠В = 180º – φ;

∠В = 180º -150º = 30º;

sin 30º = 1/2;

S = 1/2 * 4 * 6 * 1/2 = 6 cm2.

Answer: the area of ​​the triangle is 6 cm2.