Given a triangle ABC, angle C = 90 degrees, AC = 8, CH-height and right angle, CH = 4.8 Find: Area ABC.

1. According to the condition of the problem given: in a right-angled triangle ABC AC = 8, the height from the right angle C HC = 4.8.

It is known that the area of a right-angled triangle is half the product of its legs.

2. From the obtained triangle AНС according to the known leg CH and hypotenuse AC, we calculate the value sin A = 4.8: 8 = 0.6, whence the angle A = 37 ° according to the table.

Now you can find tg A = tg 37 ° = 0.75, so BC: AC = 0.75, or BC = AC * 0.75 = 5.6.

3. Let’s calculate what the area is equal to S = 1/2 AC * BC = 1/2 * 5.6 * 8 = 1/2 * 44.8 = 22.4.

Answer: The area of triangle ABC is 22.4 units ².