If you want more of a challenge, you can go head-to-head with the T. rex or try to outrun it as you throw the switches to open the various gates. A few players reminded me of a trick from the movie Jurassic Park that also works here.
After picking up the key, roll and move up onto the edge of the nest. Then throw a flare down on the ground to the left, near the ledge where you found the last medi pack.
NOTE: To use a flare, press comma [,] on the keyboard or Select + R1 on the PS1 controller to. Press the same button again to throw the flare in the direction Lara is facing. To drop a flare on the spot, light it then draw weapons and Lara will just let the flare fall instead of throwing it.
Immediately jump down out of the nest and start running around the shallow edge of the pool.
The T. rex will usually (though not always) be distracted by the flare. This only lasts a few moments, so keep moving.
Run across the open area with the raptor carcass and into the alcove with the first switch. When you took the key, the gate opened and the torch on the wall lit, showing you where to go.
Pull the switch to open the gate on the other side of the cave.
The switch alcove is too small for the T. rex to enter, so this is another safe spot from which you can shoot.
When the T. rex wanders off to the other side of the cave, you can then run out...
...and throw down another flare in the area near the dead raptor.
Then run past the T. rex as she goes to investigate the flare. Run and jump across the pool.
The gate in the far left corner is now open, and the torch above it is lit. Enter the alcove and pull the second switch.
This opens the third gate, back at the first switch, letting in another raptor from the upper level (2 or 3 raptors if you didn't kill the others before). If you stay in the switch alcove or wade into the deeper water, the T. rex should finish off the raptor for you.
Then you can throw down another flare to distract the T. rex as you make a run for the first switch.
With the third gate open, you can pick up more flares and a small medi pack on the stairs, assuming you didn't get them earlier. Then continue to the upper area...
...and either finish off the T. rex from above, or just leave her to mind her own humongous business.