Question

Высота правильной четырехугольной пирамиды вдвое меньше длины ее бокового ребра. Найдите угол между плоскостью основания пирамиды и ее боковым ребром. Помогите пожалуйста.

Answer 1

30 градусов., т.к катет против угла 30 град. равен половине гипотенузы. Высота - катет, боковая грань - гипотенуза.

Answer 2

Finding the Height of the Pyramid

To find the height of the pyramid, we can use the given information that the height is half the length of its lateral edge. Let's denote the height as h and the length of the lateral edge as l.

According to the given information, we have the equation: h = l/2.

Finding the Angle between the Base and the Lateral Edge

To find the angle between the base and the lateral edge of the pyramid, we need to use trigonometry. Let's denote the angle as θ.

We can use the formula: cos(θ) = h/l.

Substituting the value of h from the previous equation, we get: cos(θ) = (l/2)/l = 1/2.

To find the value of θ, we can take the inverse cosine (arccos) of both sides of the equation: θ = arccos(1/2).

Calculating the Angle

Using a calculator or a trigonometric table, we can find the value of θ.

According to the search results, the value of θ is approximately 60 degrees.

Therefore, the angle between the plane of the base of the pyramid and its lateral edge is approximately 60 degrees.