Triangle ABC has angle B 45 degrees, side AB 9 and side BC .

The area of ABC is:

And since side AC is:

... the circle containing triangle ABC has the radius:

Would be great to get some insight on this. I'm completely lost as to what to do.

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- Jan 23rd 2010, 09:27 PMdavidmanTriangle in circle?!
Triangle ABC has angle B 45 degrees, side AB 9 and side BC .

The area of ABC is:

And since side AC is:

... the circle containing triangle ABC has the radius:

Would be great to get some insight on this. I'm completely lost as to what to do. - Jan 23rd 2010, 10:20 PMProve It
- Jan 23rd 2010, 10:31 PMdavidman

and looking at triangles with special angles 45 and 90 tells me that

how to get side AC? I only know that one angle... - Jan 23rd 2010, 10:44 PMProve It
- Jan 23rd 2010, 11:03 PMdavidman

ok, managed with that somehow... about the circle though, is there a rule for that? - Jan 23rd 2010, 11:15 PMProve It
- Jan 23rd 2010, 11:22 PMdavidman
Yes, like http://upload.wikimedia.org/wikipedi...cribed.svg.png

wasn't sure what it's called in English, but I guess circumscribed circle of a triangle. - Jan 23rd 2010, 11:34 PMProve It
OK I don't know if there's an easier way, but here goes:

I placed the length of 9 units along the axis of a set of cartestian axes, beginning at the origin.

So that means that two of the vertices lie at and .

There is also an angle of made with the axis, and a length of units.

Using some trigonometry, I know that the final vertex must have co-ordinate

.

So now you have the three vertices as co-ordinates.

Substitute the three co-ordinates into the general equation for the circle

.

You will end up with three equations in three unknowns that you will need to solve simultaneously. One of them ( ) is the radius of the circle. - Jan 24th 2010, 12:52 AMdavidmanQuote:

Originally Posted by**Wikipedia @ http://en.wikipedia.org/wiki/Law_of_sines#Relation_to_the_circumcircle**

or in my case;

so I guess wikipedia helped save the day this time.(Giggle)