Question

If an 8-foot ladder is leaned against a wall with its foot braced 4 feet from the wall's base, how far up the wall will the top of the ladder reach? round to the nearest hundredth.

Answer 1

we know that
see the picture to better understand the problem
in the right triangle ABC
Applying the Pythagoras Theorem
AB²=BC²+AC²-------> BC²=AB²-AC²
AB=8 ft
AC=4 ft
BC²=8²-4²-----> BC²=48--------> BC=√48-------> BC=6.93 ft

the answer is
6.93 ft