Tammy is mountain climbing with Nicole and just climbed an 8 meter rock face Nicole is standing 8 meters away from the bottom cliff looking up at Tammy . How far away are Tammy and Nicole

  8√2 ≈ 11.31 meters

Step-by-step explanation:

The straight-line distance is the hypotenuse of an isosceles right triangle with legs 8 meters. So, the distance is 8√2 meters, about 11.31 meters.

Of course, you know that a right triangle with legs 1 and 1 has a hypotenuse of  ...

  √(1² +1²) = √2 . . . . . given by the Pythagorean theorem

Scaling this by a factor of 8 meters gives you legs of 8 meters and a hypotenuse of 8√2 meters.