thanks
Cut off thetwo right triangles of the trapezium (see attachment)
Then you know
(A) $\displaystyle \dfrac hx=\tan(72^\circ)$ ........ and ........ (B) $\displaystyle \dfrac hy = \tan(68^\circ)$
According to my sketch you can see that
$\displaystyle x+y=8~\implies~y=8-x$
Solve the equations (A) and (B) for h and substitute (8-x) instead of y:
$\displaystyle x\tan(72^\circ) = (8-x) \tan(68^\circ)$
Solve for x. I've got $\displaystyle x \approx 3.5659$ and consequently $\displaystyle y \approx 4.4341$ and $\displaystyle h \approx 10.9747$
I'll leave the rest for you.