Let us look at the image attached:
We can see that the height of the cone is 25.3 units and the diameter of the base is 10.4 units.
Now, the diameter of the base is 10.4 units so the radius of the base is given by [tex]\frac{10.4}{2} =5.2[/tex]
From the figure attached we can see that the height of the perpendicular in the triangle is 25.3 units and the length of the base is 5.2 units.
So, the angle made by the side of the cone with the base is given by
[tex]tan \Theta =\frac{25.3}{5.2}[/tex]
[tex]tan \Theta =4.865[/tex]
[tex]\Theta =tan^{-1}(4.865)[/tex]
[tex]\Theta =78.384^{\circ}[/tex]
Therefore, the side of the cone makes [tex]78.384^ \circ[/tex] with the base of the cone.
