Question

Стороны треугольника АВС. АВ =8; ВС =10 ;АС =12. . опредилите вид реугольника АВС

Answer 1

Это прямоугольный треугольник

Answer 2

Triangle ABC

To determine the type of triangle ABC, where AB = 8, BC = 10, and AC = 12, we can use the triangle inequality theorem and the Pythagorean theorem.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's verify this for the given sides of triangle ABC.

According to the triangle inequality theorem: - AB + BC > AC - AB + AC > BC - BC + AC > AB

Let's calculate these inequalities: - 8 + 10 > 12 - 8 + 12 > 10 - 10 + 12 > 8

All these inequalities hold true, so the given sides satisfy the triangle inequality theorem.

Type of Triangle ABC

Now, let's use the Pythagorean theorem to determine the type of triangle ABC. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can calculate whether triangle ABC is a right-angled triangle using the given sides: - AB^2 + BC^2 = AC^2 - 8^2 + 10^2 = 12^2 - 64 + 100 = 144 - 164 = 144

Since 164 is not equal to 144, triangle ABC is not a right-angled triangle.

Conclusion

Based on the calculations, triangle ABC with sides AB = 8, BC = 10, and AC = 12 is an ordinary scalene triangle since all sides have different lengths and none of the angles are right angles.