make a diagram
Triangle ABC with AB=17, BC=8 and AC = 15
Did you realize that your triangle is right-angled, with angle C = 90° ?
let the points of contact of the circle be
D on BC, E on AC, and F on AB
Two properties we can use ...
1. The centre of the incscribed circle lies on the angle bisectors of the triangle, and
2. BF=BC , AE=AF, and DC = EC, by the tangent properties
let the radius be r,
since the 90° is bisected, DC = r
then BD= 8-r, and of course by #2 BF=8-r
then AF= 9+r and AE = 15-r
I see two similar triangles at the top, so
r/(9+r) = r/(15-r)
solve for r