need help finding apothem of reg. octogon w/ 10" sides

[JayJay06]

I need some one with this problem:

Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are each 10 inches long.

Thanks for the help.

 

[skeeter]

break up the regular octagon into eight isosceles triangles with common vertex at the center ...

the vertex angle = 360/8 = 45 degrees

the base angles of each triangle are each (180-45)/2 = 67.5 degrees

the base of each isosceles triangle is 10 inches.

the apothem is the height of the isosceles triangle, from the vertex angle perpedicular to the base ... sketch it in, you now have a right triangle.

using your trig ratios ...

tan(67.5) = h/5 or h = 5tan(67.5), the length of the apothem.

 

[JayJay06]

so my answer is 29.5

 

[jwpaine]

so my answer is 29.5

What are the steps you took to get that?

5tan(67.5) is NOT equal to 29.5