Connected right triangles

A right-angled triangle has hypotenuse 29 and vertical leg 20; its base is split equally at \(R\). From \(R\), a second right-angled triangle has vertical leg 6; find the half-base \(m\) and its hypotenuse \(n\).[3]

All lengths are in centimetres. Give non-exact answers to 3 significant figures unless an exact value is requested.