[Beau1953]

The angle is 45 degrees. 2 sides of the triangle is 3 feet long. How long is the third side?

[robertva]

Since two sides are three feet you have an isosceles triangle (two sides the same length). But you don't say if you have ONE 45° angle between the two 3 foot sides OR 45° angles on the other two corners.

This leaves two DIFFERENT possibilities. It could be an isosceles right triangle with one 90° angle and two 45° angles OR an isosceles triangle with only one 45° angle and two 67 1/2° angles

The hypotenuse of an isosceles right triangle ( 45 X 45 X 90) is 1.414 times the length of either of the remaining legs. 3 * 1.414 = 4.243

The short leg of a 22 1/2° and 67 1/2° right triangle is 0.383 (sin22°) times the hypotenuse. 3 * 0.383 = 1.148. But Your triangle (if 45 X 67.5 X 67.5) is the same as two of these together so 2 * 1.148 = 2.296

[Beau1953]

RobertVA,
Thanks for the answer and I apologise for not being clear on the questuion. This was the scenerio I was looking for. But Your triangle (if 45 X 67.5 X 67.5) is the same as two of these together so 2 * 1.148 = 2.296

I am designing a flower bed around a tree. The tree is 3 feet in diameter. I am making the Diameter of the bed 6 feet. Dividing that circle in 8 parts make eaxh angle from the center at 45 degrees. As you pointed out to me that leaves 67.5 and 67.5 for the other t andles, since I don't have curved boards for the perimeter. I needed to know how long the 8 side pieces would be. You solved it for me. Thanks again
Beau