Calculate the area of a triangle whose two sides are 3 cm and 2 cm, and the angle between them is 30 *.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle B = 30 °. Side AB = 3 cm. Side BC = 2 cm.

2. From the top A we draw the height AH to the side BC.

3. We calculate its length through the sine of angle B of triangle ABH, in which AH leg, located opposite angle B, AB is the hypotenuse:

sine 30 ° = AH / AB.

AH / AB = 1/2.

AH = 3 x 1/2 = 1.5 cm.

4. The area of the triangle ABC = AH x BC: 2 = 1.5 x 2: 2 = 1.5 cm ^ 2.

Answer: the area of the triangle ABC is 1.5 cm ^ 2.