After walking through the fifth gate, your computer informs you that more than half of the gates have been crossed. "Only $4$ left", you conclude. "Computer, what is this gate's riddle?"$$

Your computer responds:

For the function,$$f$($t$)=1/$a$(5$t$^339$t$^2+117)^45,$ find the value of a$$that would make the slope of the tangent line$180$ at$$t$=2$