Irregular Cone Geometry Problem: Finding the Area of an Elliptical Base

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SUMMARY

The discussion focuses on calculating the area of the base of an elliptical, non-right cone using two parameters: the length from the center of the ellipse to the vertex and the angle of the cone's sides. The area can be determined using the formula A = πab, where 'a' and 'b' represent the semi-major and semi-minor axes of the ellipse. Participants suggest employing trigonometric methods to derive the lengths of these axes by creating a right triangle from the cone's vertex.

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  • Understanding of elliptical geometry
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  • Knowledge of cone properties
  • Ability to apply geometric formulas
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Appity
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Homework Statement



I'm wondering whether or not it is possible to get the area of the base of an elliptical, non-right cone if the following two parameters are known:

- length from center of ellipse up to vertex
- angle that the sides make

Here is a simple visual: http://i.imgur.com/M6jT5.png

Homework Equations



A=\pi ab

The Attempt at a Solution



I've tried looking at geometry guides with no success. I'm thinking I might be able to use some clever trig and drop a right angle down from the vertex in order to get the length of the semi-minor/major axis, but I can't reason it out. any advice would be appreciated.
 
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Hi Appity! :smile:

Hint: slice the cone so that you get a circular cross-section, then use trig to find the area of the projection. :wink:
 

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