Applying Triig functions

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heatherkerr8390

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We are using angles of elevation and anges of depression...
we are also using right triangle trig...
I'm SOOOOOOOOOOO stuck on this problem.. and most like it.. I just want to cry pleeease help!

It says that a regular hexogon is inscribed in a circle w/ the diameter 6.4 centimeters...
Letter A says to find the apothem of the hexongon.. wouldn't you have to find the circumference?? Isnt apothem the same as the circumference??
I put c=2(pie)R ................ c=2(3.14)3.2 = 20.096........

Then, B says to find the length of a side of a hexagon... there doesnt seem to be enough info... HELP.... cause there is a C and D too.... I'm so lost... =[
 
One way to inscribe a regular hexagon in a circle is to draw the circle with a compasses. Then, without changing the radius simply place the point of the compasses on the circle and scribe an arc on the circle. Then place the point of the compasses on that arc where it intersects the circle and scribe another arc. Place the point of the compasses on this new arc and scribe another arc, etc. You end up with six equally spaced arcs intersecting the circle. Draw your hexagon sides between adjoining points where the arcs intersect the circle and you have a regular hexagon. Now, with careful observation, you will note that each side of the hexagon is the same length as the radius of the circle. If you were to draw in radii to each vertex of the hexagon, what kind of triangles would you have? Now, draw in an apothem. What kind of a right triangle do you have? Can you use the Pythagorean Theorem to answer your question?
 
We havent done anything with arcs....
you would have 5 triangles w/ all the same sides...
Isnt the apothem the same as the circumference??
I dont think so...
If they all had the same side, it would work... but I cant get the length of the side w/ just the radius or the circumference....
there isnt enough information....
 
heatherkerr8390 said:
We havent done anything with arcs....
you would have 5 triangles w/ all the same sides... <<< No you would get 6 triangles - "hex" means six.

Isnt the apothem the same as the circumference?? No - go to http://en.wikipedia.org/wiki/Apothem to see definition of apothem
I dont think so...
If they all had the same side, it would work... but I cant get the length of the side w/ just the radius or the circumference....
there isnt enough information....
Click to expand...

Draw the hexagon using a compass - like Loren suggested - then think. It will become clear.

The sides of the hexagon is equal to the radius.
 
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