Compound right-triangle lengths

All lengths are in centimetres. Find the unknown lengths, giving non-exact answers to 3 significant figures.

1. A right-angled triangle has hypotenuse 15 and base 9; its height is \(u\). An adjacent right-angled isosceles triangle has legs \(u\), so its hypotenuse is \(v\).
2. 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. On base \(BD=30\) cm, \(BC=x\) and \(CD=8\) cm. Right-angled triangle \(ABC\) has hypotenuse \(AB=25\) cm. Point \(E\) lies on \(AC\), with \(EC=6\) cm; find \(x=BC\) and \(y=AE\).
4. A rectangle has width 16 and diagonal 20. Find height \(p\) and the distance \(q\) from a corner to the midpoint of the opposite vertical side.