Expert: Sherman D. - 6/12/2007

Question
An extention ladder adjusts in length from 10 feet to 16 feet. Suppose you've leaned your ladder against your house so that at its minimum length, it touches the base of your first floor window, 9 feet above the ground. Without moving the base, how high will the ladder reach when extended (to the nearest decimal)?

Answer
a^2 + b^2 = c^2
9^2 + b^2 = 10^2
81 + b^2 = 100
b^2 = 19
b = sqrt(19) or about 4.3589

this means to be at its most minimum length it would have to be at about 4.36 ft from the house.

Without moving the ladder from this point

16^2 + sqrt(19)^2 = c^2
c^2 = 256 + 19
c^2 = 275
c = 16.583 ft or about 16.6 ft is the height that it will reach.

It helps to picture it or draw it out.