Q.47 see image.........................................................

r1= K/(s – h) and R= abh/4K where K is area and R is circumradius and r1 is exradius. obviously K= ab/2. so that R= h/2

so ratio R/r1= h(s – h)/2K= h(s – h)/ab= root2/(root2 + root3)

now, let a/b= x and by pythagoras a^2+b^2= h^2 or h= b*root(1+x^2)

also, 2s= a+b+h

so you can plug in these values in terms of x and you shall get the ratio. finding angles B and C is easy as tan B and tanC can be found out once the value of x is known.