On the other hand, Abraham was considered righteous BECAUSE of his belief.
If you do not trust God, that means you are trusting in something other than God, be it yourself, some other human, or the devil himself. Place your trust and belief in God, and He will amaze you with His provision and protection for you.
Keep in mind, though, that God does not necessarily remove obstacles and trials from us. But He does walk with us through them.
The three Hebrew boys were commanded to worship a statue that Nebbechadnezar set up. They refused, and because they refused they were cast into a furnace. They told Nebby that their God was able to deliver them, and even if He didn't deliver them, they would not worship the statue. Nebby through them in. God did not prevent them from being thrown in, even though they believed in and trusted Him.
But once in there, He protected them from the flames, and they came out not even smelling like smoke. God used that situation not only to strengthen the faith of those boys, but also as a testimony to His power. Nebby and everyone else knew God had protected them, and could plainly see that God was so much more powerful than their foolish statue.