# Math Help - trapezoid

1. ## trapezoid

thanks

2. Originally Posted by helloying
thanks
Cut off thetwo right triangles of the trapezium (see attachment)

Then you know

(A) $\dfrac hx=\tan(72^\circ)$ ........ and ........ (B) $\dfrac hy = \tan(68^\circ)$

According to my sketch you can see that

$x+y=8~\implies~y=8-x$

Solve the equations (A) and (B) for h and substitute (8-x) instead of y:

$x\tan(72^\circ) = (8-x) \tan(68^\circ)$

Solve for x. I've got $x \approx 3.5659$ and consequently $y \approx 4.4341$ and $h \approx 10.9747$

I'll leave the rest for you.