Question 1068092


the slant height of the right circular cone makes an angle A with the base.
the slant height measures 30mm and it is 3 times the measure of the radius of the base.


this means the radius of the base must be 10 mm, if i understand you correctly.


drop a perpendicular from the vertex of the cone to the center of the base and you have a right triangle formed with the radius of the base as one leg and the slant height as the hypotenuse.


cosine of angle A is equal to the adjacent side divided by the hypotenuse.


this becomes cos(A) = 10/30 = 1/3.


use your calculator to solve for A to get A = 70.52877937 degrees.