Question

Помогите пожалуйста решить Основанием треугольной пирамиды МАВС ЯВЛЯЕТСЯ ПРЯМОУГОЛЬНЫЙ ТРЕУГОЛЬНИК АВС с гипотенузой АВ=10 И КАТЕТОМ ас = 8. Боковые ребра пирамиды образуют с высокой пирамиды равные углы в 45 градусов. Найдите объем пирамиды.

Answer 1

Всё решаем по формулам..........

Answer 2

Finding the Volume of a Triangular Pyramid

To find the volume of a triangular pyramid, we need to know the base area and the height of the pyramid. In this case, the base of the pyramid is a right-angled triangle ABC, with hypotenuse AB measuring 10 units and one of the legs, AC, measuring 8 units. The lateral edges of the pyramid form equal angles of 45 degrees with the height of the pyramid.

To find the height of the pyramid, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

AC^2 + BC^2 = AB^2

Substituting the given values, we have:

8^2 + BC^2 = 10^2

Simplifying the equation, we get:

64 + BC^2 = 100

BC^2 = 100 - 64

BC^2 = 36

Taking the square root of both sides, we find:

BC = 6

So, the length of the other leg of the right-angled triangle ABC is 6 units.

Now that we have the base dimensions of the pyramid (8 units and 6 units), we can find the base area. The area of a right-angled triangle is given by the formula:

Area = (base * height) / 2

In this case, the base is 8 units and the height is 6 units, so the base area is:

Area = (8 * 6) / 2 = 24 square units.

Finally, we can calculate the volume of the pyramid using the formula:

Volume = (base area * height) / 3

Substituting the values, we have:

Volume = (24 * 6) / 3 = 48 cubic units.

Therefore, the volume of the given triangular pyramid is 48 cubic units.