Question

a 10 ft ladder leans against a wall with its foot braced 3ft. from wall's base how far up the wall does the ladder resach

Answer 1

Ladder makes a right triangle with the wall and ground. The hypotenuse = length of the ladder = 10 ft 
Let the height be h
By Pythagorean theorem 
10^2 = 3^2 + h^2 
h^2 = 10^2 - 3^2 = 100 - 9 = 91
h = sqrt( 91) = 9.54 ft