If you want to get to the Sugar Loaf cable car ticket office 100% safely, it is best to take a taxi, which will cost you approximately R$16; US$8.50; €7 from Copacabana and R$22; US$13; €10 from Ipanema. Cabs in Rio de Janeiro are fast, reliable and rather inexpensive if compared to other cities (even in Brazil).
A taxi ride will take between 10 and 30 minutes, depending on traffic and your departure place at either neighborhood. Equally safely are, of course, Sugar Loaf Mountain guided tours recommended by a reliable source.
Click here for photos of both: Sugar Loaf and Christ the Redeemer statue atop Corcovado Mountain as well as for practical information and basic history.