The radius of the base of the conua is 5 cm, its height is 12 cm. Find the perimeter of the axial section

The radius of the base of the conua is 5 cm, its height is 12 cm. Find the perimeter of the axial section, the length of the forming angle of its inclination to the plane of the base.

Since the cone is formed as a result of the rotation of a right-angled triangle, its axial section is also a triangle, only isosceles.

First, we find the length of the generator using the Pythagorean theorem:

L ^ 2 = r ^ 2 + h ^ 2;

L ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169;

L = √169 = 13 cm.

In order to find the angle of inclination of the generatrix to the plane, we apply the theorem of sines:

sin A = h / L;

sin A = 12/13 = 0.92 ≈ 67º.

The perimeter of an axial section is the sum of the lengths of all its sides:

P = 13 + (5 + 5) + 13 = 13 + 10 + 13 = 36 cm.

Answer: the perimeter of the axial section is 36 cm, the generatrix is ​​13 cm, the angle of its inclination is 67º.