$8\mathrm{.}3\mathrm{.}9.$ A V$-$canyon supports a $100-$ft high, constant$-$angle $(120)$ arch dam. If the canyon is $60$ ft wide at the top and the design freeboard is $6$ ft $($i$.$e$.,$ the water level is $6$ ft below the top of the dam$),$ determine the abutment reactions at dam heights of $25,50,$ and $75$ ft above the bottom of the canyon.

THE CORRECT ANSWER IS:

@$25$ ft$,37,200$ lb$/$ft

@$50$ ft$,47,400$ lb$/$ft

@$75$ ft$,30,800$ lb$/$ft