Question

Высота правильной треугольной пирамиды sabc и сторона основания равны 16 и 10 соответственно. Найдите тангенс угла между боковым ребром и плоскостью Пожалуйста помогите, желательно с рисунком

Answer 1

Решение смотрите в закрепленной фотографии.

Answer 2

Finding the Tangent of the Angle between the Lateral Edge and the Base Plane of a Regular Triangular Pyramid

To find the tangent of the angle between the lateral edge and the base plane of a regular triangular pyramid, we need to use the given information about the height and side length of the base.

Let's denote the height of the pyramid as 'h' and the side length of the base as 's'. In this case, the height 'h' is 16 and the side length 's' is 10.

To find the tangent of the angle, we can use trigonometric ratios. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, the lateral edge of the pyramid is the opposite side, and the distance from the apex of the pyramid to the center of the base is the adjacent side.

To find the length of the lateral edge, we can use the Pythagorean theorem. The lateral edge is the hypotenuse of a right triangle formed by the height 'h' and half the side length of the base 's/2'.

Using the Pythagorean theorem, we can calculate the length of the lateral edge as follows:

lateral edge = sqrt(h^2 + (s/2)^2) Substituting the given values:

lateral edge = sqrt(16^2 + (10/2)^2) = sqrt(256 + 25) = sqrt(281)

Now that we have the length of the lateral edge, we can find the tangent of the angle using the formula:

tangent(angle) = opposite/adjacent = lateral edge / (s/2)

Substituting the values:

tangent(angle) = sqrt(281) / (10/2) = 2 * sqrt(281) / 10

Therefore, the tangent of the angle between the lateral edge and the base plane of the pyramid is 2 * sqrt(281) / 10.

Unfortunately, I couldn't find a suitable diagram to illustrate this. However, I hope the explanation provided is clear. Let me know if you have any further questions!