In triangle ABC, side AB = 6√3 cm, AC = 8 cm, angle A = 60 degrees. Find the area.

1. From the vertex B of the triangle ABC we draw the height of the HВ to the side of the AC

2. In a right-angled triangle, the ВН leg is opposite an angle equal to 60 ° according to the problem statement. According to the properties of a right-angled triangle, the ratio of the opposite leg to the hypotenuse is equal to the sine of this angle:

ВН / AB = sinus 60 °.

BH = AB x √3 / 2 = 6√3 x √3 / 2 = 9 centimeters.

3. Calculate the area of the triangle ABC:

AC x BН / 2 = 9 x 8/2 = 36 cm ^ 2.

Answer: the area of the triangle ABC is 36 cm ^ 2.