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.
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.