So, I saw this question in a book,
You have been given a cone. The cone's base angles are both equal to 75° and the vertical angle is (of course) 30°.The radius of the cone is 7 metres.Now, you cut the cone's top 1/3rd and are left with 2/3rd of it(the frustum). Calculate the slant height of the cone and also calculate the radius of the top surface formed after converting it into a frustum.
Couldn't really understand how to do it. I'm just a High School student, so I'm not much aware as to how to solve such questions, so help requested here. Also, I was given the clue by a maths teacher that you may like to use Trigonometry, which I'm not really good at, so help out here. Thanks in advance, Nalin Bhardwaj
Hint: If you slice the cone with a plane through the axis, you have a $30-75-75$ triangle. Bisecting the $30^\circ$ angle gives two right triangles. You have the short leg from the radius, and trig will give the other legs-you need the tangent of $75^\circ$. The hypotenuse is the slant height. Presumably the top third you cut off is the top third of the altitude (not the volume), so that will make a similar triangle, giving the top radius. This is entirely a 2D problem once you slice the cone.