The two sides of the triangle are 4√3cm and 6cm, and the angle between them is 60 degrees.

The two sides of the triangle are 4√3cm and 6cm, and the angle between them is 60 degrees. Find the area of the triangle.

From the top B we will draw the height ВН. In a right-angled triangle ВСН, the angle СН = 180 – 90 – 60 = 30. The leg СН lies opposite the angle 30, and is equal to half the length of the hypotenuse BC.

CH = 4 * √3 / 2 = 2 * √3 cm.

Then, by the Pythagorean theorem, BH ^ 2 = BC ^ 2 – CH ^ 2 = 48 – 12 = 36.

BH = 6 cm.

Determine the area of the triangle: Sавс = АС * ВН / 2 = 6 * 6/2 = 18 cm.

Answer: The area of the triangle is 18 cm2.