I have a regular octagon with a radius of 9.

I have split the 8 pie slices into right angles--leaving angles 90, 67.5, and 22.5. I looked for the sine of 22.5 opp/hyp and get .38. Then the oppositeside is 6.84. I can't get the right answer, what am I doing wrong?
Thanks

not sure what you're doing wrong, because you haven't said what you are trying to do. But if you want the side length, then if it is s, then you do have

(s/2)/9 = sin(22.5)
s = 18*.3826 = 6.888

I figured out my mistake. With thearea of the triangle, I forgot the .5

thanks steve, sometimes you need another perspective.

To find the length of the opposite side of an angle in a regular polygon, you'll need to use the trigonometric functions. In this case, you have correctly identified that you need to use the sine function.

However, there seems to be a mistake in your calculations. The sine of 22.5 degrees is not 0.38. Instead, the correct value is approximately 0.3827.

To calculate the opposite side length, you can use the sine formula:

opposite side = hypotenuse * sin(angle)

Given that the radius of the octagon is 9 and the sine of 22.5 degrees is approximately 0.3827, you can calculate the opposite side length as follows:

opposite side = 9 * 0.3827
opposite side ≈ 3.4459

So, the length of the opposite side is approximately 3.4459 units, not 6.84. Therefore, it seems that your mistake lies in calculating the sine value for the angle.