In a right-angled triangle ABC with a right angle A, the height AH is dropped to the hypotenuse BC.

In a right-angled triangle ABC with a right angle A, the height AH is dropped to the hypotenuse BC. Find the area ABC if BH = 6 HC = 2.

1. ВС = ВН + СН = 6 + 2 = 8 units of measurement.

2. According to the properties of a right-angled triangle, the height BH, drawn from the vertex of the right angle, is calculated by the formula: BH = √BH x CH = √6 x 2 = √12 = √4 x 3 = 2√3 units.

3. The area of the triangle ABC is equal to half the product of the length of the hypotenuse BC by the length of the height AH: the area of the triangle ABC = BC x AН: 2 = 8 x 2√3: 2 = 8√3 units of measurement ^ 2.

Answer: the area of the triangle ABC is 8√3 units of measurement ^ 2.