1) The base of a 10-ft ladder stands 6 feet from the base of a house. Will the ladder reach 7 feet high? Justify your answer.
10 ft
6 ft

Phytagoras theorem
a^2 + b^2 = c^2
where c is the hypotenuse; angle between a and b is 90 degrees.
In this case, c = 10 ft
Say a = 6 ft
then find b
6^2 + b^2 = 10^2
b^2 = 100 - 36 = 64
b = 8 ft
So yes, it will reach over 7 feet