who gave the approval to build it?
Congress
Hoover Dam
Even before Congress approved the Boulder Canyon Project, the Bureau of Reclamation was considering what kind of dam should be used. 
where does the energy from the hoover dam go The dam's generators provide power for public and private utilities in Nevada, Arizona, and California. where is it located? In the Black Canyon of the Colorado River on the border between the U.S. states of Nevada and Arizona. when was it built? Between 1931 and 1936
wiki:7741965
Hoover Dam [SEP] Design, preparation and contracting
Even before Congress approved the Boulder Canyon Project, the Bureau of Reclamation was considering what kind of dam should be used. Officials eventually decided on a massive concrete arch-gravity dam, the design of which was overseen by the Bureau's chief design engineer John L. Savage. The monolithic dam would be thick at the bottom and thin near the top, and would present a convex face towards the water above the dam. The curving arch of the dam would transmit the water's force into the abutments, in this case the rock walls of the canyon. The wedge-shaped dam would be thick at the bottom, narrowing to at the top, leaving room for a highway connecting Nevada and Arizona.