College Algebra Word Problem

Question

A building is 1 ft from a 12-ft fence that surrounds the property. A worker wants to wash a window in the building 16 ft from the ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 7 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

Answer 1

you have a right triangle

the vertical leg is 16 feet

the horizontal leg is 1+7=8 feet

the hypotenuse is the length of the ladder, call it x

x^2=16^2+8^2

x^2=256+64

x^2=320

√x^2=√320

x=√(64*5)

x=8√5

x=8*2.236

x=17.888

x=17.8 feet (or just find √320 which is 17.888544)