The triangle ABC is right triangled at A. Ratio of the radius of the circle circumscribed to the radius of the circle escribed to the hypotenuse is √2 : (√3 + √2). Find the angles B & C and the ratio of the two perpendicular sides of the triangle.
(This involves trigonometry, doesn't it? But where? And how?....)
it appears that the ratio you have quoted is wrong.
Circumradius= a/2
radius of circle escribed to the hypotenuse=
a.(cos(B/2).cos(C/2))/(cos(A/2))
On taking the ratio and equating with the given ratio you will get
2cos(B/2).cos(C/2) = sqrt(3)+sqrt(2) > 2(Never possible)
Hence,your question appears wrong .
Would you mind specifying the source of this question