# Question #bcedf

##### 1 Answer

Length of each side is 248.53 mm 2.d.p.

Interior angle is

#### Explanation:

I don't know if I will be able to explain this with words alone. This is where you desperately need geometrical diagrams. I'll try my best.

If you construct isosceles triangles on the inside of the octagon the angle at there apex will be:

This gives

We know the length of one side of this triangle, because it will be the length of the radius, which is

We now have a right angled triangle with angles

Sum of interior angles is:

Where

So:

Each angle is then:

Half this angle to get the third angle of the triangle:

We now have a right angled triangle with angles

If we label the sides of the triangle a b c ( c being the hypotenuse ) and opposite angles A B C respectively.

We need to find the length of side a.

Using the Sine Rule

Rearranged gives:

4 .d.p.

This is HALF the length of one of the sides of the octagon, so:

2 .d.p.

So we have:

Length of octagon side 248.53mm.

Interior angle

Hope this helps you. It would have been much easier for me and for you if we could have used diagrams.