Question

Help, please)) Тесты по геометрии. 7 класс (Фарков)Тема 5. Вариант 1.В3. В прямоугольном треугольнике АВС угол А=90 гр., АВ= 6 см, АС=10 см. Расстояние от точки В до прямой АС будет равно...В7. Часть схемы  решения задачи на построение, в которой отыскивается способ решения задачи на построение.

Answer 1

Task 1: Finding the distance from point B to line AC in a right triangle ABC

To find the distance from point B to line AC in a right triangle ABC, we can use the formula for the distance between a point and a line. In this case, point B is not on line AC, so we need to find the perpendicular distance from point B to line AC.

Given: - Angle A = 90 degrees - AB = 6 cm - AC = 10 cm

To find the distance from point B to line AC, we can use the formula:

Distance = (Area of triangle ABC) / (Length of base AC)

First, let's find the area of triangle ABC using the formula:

Area = (1/2) * (Length of base AC) * (Length of height BH)

In a right triangle, the height BH is equal to the length of the side AB. Therefore, the area of triangle ABC is:

Area = (1/2) * AC * AB

Substituting the given values:

Area = (1/2) * 10 cm * 6 cm = 30 cm^2

Now, let's find the length of base AC. Since AC is the hypotenuse of the right triangle, we can use the Pythagorean theorem:

AC^2 = AB^2 + BC^2

Substituting the given values:

10 cm^2 = 6 cm^2 + BC^2

Simplifying the equation:

BC^2 = 10 cm^2 - 6 cm^2 = 4 cm^2

Taking the square root of both sides:

BC = 2 cm

Now we have all the values we need to find the distance from point B to line AC:

Distance = Area / AC = 30 cm^2 / 10 cm = 3 cm

Therefore, the distance from point B to line AC in the given right triangle ABC is 3 cm.

Task 7: Part of the solution scheme for a construction problem

Unfortunately, the specific details of the construction problem and the solution scheme you mentioned are not provided in your question. To provide a more accurate response, please provide more information about the construction problem and the specific part of the solution scheme you would like to discuss.