a regular triangular pyramid has all of edges of length 36. What is the angle between any two faces of this pyramid.

the answer is 70.529

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u have to imagine a right triangle there.

To find the angle between any two faces of a regular triangular pyramid, we can start by determining the type of triangle formed by the base. Since all the edges of the pyramid have a length of 36, the base is an equilateral triangle, where all three sides are equal.

In an equilateral triangle, all three internal angles are also equal and have a value of 60 degrees. Therefore, each angle of the triangular base is 60 degrees.

Next, we need to determine the angle between one of the triangular faces and the base. In a regular triangular pyramid, the triangular faces are isosceles triangles, where the base angles are equal.

To find the base angle of the triangular face, we can use the formula for the sum of the angles of a triangle:

Sum of angles in a triangle = 180 degrees

Let x represent the base angle of the triangular face. Since the triangular face has two congruent base angles and one top angle of x degrees, we can write the equation:

x + x + 60 = 180

Simplifying the equation, we get:

2x + 60 = 180
2x = 180 - 60
2x = 120
x = 120 / 2
x = 60

Therefore, the base angle of the triangular face is 60 degrees.

Finally, to find the angle between any two faces of the pyramid, we consider the angle between the base and the triangular face. Since both of these angles are equal to 60 degrees, the angle between any two faces of the pyramid is also 60 degrees.

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60 degrees