Question

В основании пирамиды DABC лежит прямоугольный треугольник ABC, угол C=90 угол А=30 ВС=10. Боковые ребра пирамиды равно наклонены к плоскости основания. Высота пирамиды равна 5. Найти площадь боковой поверхности пирамиды. РЕШИТЕ С РИСУНКОМ ПОЖАЛУЙСТА

Answer 1

Дано:
BC=10
угол С=90
угол A=30
углы DCO=BOD=AOD
h=5
-------------
Решение:
так как углы DCO=DBO=DAO
треугольники DCO=DBO=DAO
BD=CD=AD
CA=10/tg3=10√3
BA=10/sin30=20
BO=OA=CO=10
Sбок=Sвос+Sbda+Sdca=BC*DK/2+BA*DO/2+DN*CA/2=5DK+50+5√3DN=5√(5²+(BO²-BK²)²+50+5√3*(5²+(CO²-CN²)²=100+25√6

Answer 2

Problem Analysis

We are given a pyramid DABC, where the base is a right-angled triangle ABC with angle C = 90° and angle A = 30°. We are also given that BC = 10 and the height of the pyramid is 5. We need to find the lateral surface area of the pyramid.

Solution

To find the lateral surface area of the pyramid, we need to find the area of the four triangular faces.

Let's start by finding the lengths of the sides of the triangle ABC.

Using the given information, we know that angle A = 30° and BC = 10. We can use trigonometric ratios to find the lengths of the sides AB and AC.

Using the sine ratio, we have: sin(A) = AB / BC sin(30°) = AB / 10 AB = 10 * sin(30°) AB = 10 * 0.5 AB = 5

Similarly, using the cosine ratio, we have: cos(A) = AC / BC cos(30°) = AC / 10 AC = 10 * cos(30°) AC = 10 * √3/2 AC = 5√3

Now that we have the lengths of the sides AB and AC, we can find the area of triangle ABC using the formula for the area of a triangle: Area(ABC) = (1/2) * AB * AC Area(ABC) = (1/2) * 5 * 5√3 Area(ABC) = 25√3 / 2

Since the lateral surface area of the pyramid consists of four congruent triangles, each with base BC and height equal to the height of the pyramid, we can find the lateral surface area by multiplying the area of triangle ABC by 4.

Lateral Surface Area = 4 * Area(ABC) Lateral Surface Area = 4 * (25√3 / 2) Lateral Surface Area = 50√3

Therefore, the lateral surface area of the pyramid DABC is 50√3 square units.

Diagram

Here is a diagram to help visualize the pyramid DABC:

        D
       /|\
      / | \
     /  |  \
    /   |   \
   /    |    \
  /     |     \
 A------C------B

In the diagram, the base triangle ABC is a right-angled triangle with angle C = 90° and angle A = 30°. The length of BC is 10 units, and the height of the pyramid is 5 units. The lateral surface area of the pyramid is represented by the four triangular faces.

I hope this helps! Let me know if you have any further questions.