How to Calculate the Angle in a Cone with Given Height and Circumference?

[chawki]

Homework Statement

The height h of the cone is 1/3 of l the circumference of the base .

Homework Equations

Calculate the angle alpha. Give your answer with 2 decimals.

The Attempt at a Solution

h=1/3 * 2*Pi*r

and then we don't have the radius

 

[armolinasf]

you do have r, r=r. you have a right triangle with base opposite side equal to r and an adjacent side = 2pi*r/3. apply some trigonometry and you should be able to find alpha

 

[armolinasf]

I'm curious about how you're able to get an exact answer to this problem even though it's given in general terms. I hope someone could shed some light on this.

 

[chawki]

you do have r, r=r. you have a right triangle with base opposite side equal to r and an adjacent side = 2pi*r/3. apply some trigonometry and you should be able to find alpha

where did that ''adjacent side = 2pi*r/3'' came from

 

[armolinasf]

If you make a a right triangle with right angle at the base and angle alpha as the vertex. The side adjacent to angle alpha is the height of the cone which is defined as h=(2*pi*r)/3

 

[chawki]

i have to say this is new for me..can you please demostrate how to got it?
also if there is a pre-defined formula for the hypotenuese i would be glad to know it

 

[chawki]

i have to say this is new for me..can you please demostrate how to got it?
also if there is a pre-defined formula for the hypotenuese i would be glad to know it

OH my lord..i just asked to demostrate that and forgot that it was given i should go to sleep

 

[armolinasf]

Haha...we've all been there at some point, it'll probably do a world of good to get some sleep