I need to find the lateral surface area of a cone but there is no radius measure given, only the slant height and and angle. How do I find the lateral surface area with no known radius? Pls help!

Question

I need to find the lateral surface area of a cone but there is no radius measure given, only the slant height and and angle.  How do I find the lateral surface area with no known radius? Pls help!

tkhunny · Answer

Usually the tangent concept and/or the Pythagorean Theorem will be of some benefit.

imstuck · Answer

ok I can see where that would be helpful cuz the tangent is the side opposite the angle over the adjacent, but the answers they have provided in the multiple choice are in fraction form.  That part I don't get

tkhunny · Answer

Did you find the ENTIRE triangle?  There is a cone height and a cone radius.  Both can be obtained via the tangent - particularly if the angle is convenient, say 30º, 45º, or 60º.

imstuck · Answer

Splitting it in half so to speak creates 2 right triangles (actually the bottom is a bit curved because the paper used was a circular sector of paper...does that matter here?)

imstuck · Answer

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