In a triangle, one of the sides is 28, the other is 17√3, and the angle between them is 60 degrees.

In a triangle, one of the sides is 28, the other is 17√3, and the angle between them is 60 degrees. Find the area of the triangle.

1. A, B, C – the vertices of the triangle. AB = 28 units. BC = 17√3 units of measurement.

∠А = 60 °. S is the area of the triangle. AH – the height drawn to the side of the aircraft.

2. AN: AB = sine ∠A = sine 60 ° = √3 / 2.

AH = AB x √3 / 2 = 28 x √3 / 2 = 14√3 units of measurement.

3. S = BC / 2 x AH = 17√3 / 2 x 14√3 = 357 units of measurement².

Answer: the area of the triangle ABC is 357 units of measurement².