In your drawing, the 8 inch side should be at the base of the triangle.
Label the hypotenuse "C" and either of the legs of the triangle "A" and the other one "B. This is because the midpoint of the hypotenuse is the center of the circumcircle of the right triangle, and each of the two triangles created by the partition has two equal radii as two of its sides.
In ancient Greek architecture and its later imitations, the obtuse isosceles triangle was used; in Gothic architecture this was replaced by the acute isosceles triangle. Robin Wilson credits this argument to Lewis Carroll who published it inbut W. Rival explanations for this name include the theory that it is because the diagram used by Euclid in his demonstration of the result resembles a bridge, or because this is the first difficult result in Euclid, and acts to separate those who can understand Euclid's geometry from those who cannot.
The Pythagorean theorem can be used to solve for any side of an isosceles triangle as well, even though it is not a right triangle. Rouse Ball published it in and later wrote that Carroll obtained the argument from him. Draw a straight line down the middle of the triangle from the vertex to the base.