A painter leans a 15-foot ladder against a house. The base of the ladder is 5 feet from the house. To the nearest tenth of a foot, how high on the house does the ladder reach?

a) Use Pythagorean Theorem which is c^2 = a^2 + b^2 where c is the hypotenuse and a and b are the other two legs of the right triangle.

Given: 15 ft ladder is the hypotenuse, 5 ft is one leg. Find the height of the house the ladder reaches which is the other leg of the triangle, call it b.

15^2 = 5^2 + b^2.

225 = 25 + b^2. Subtract 25 from both sides of the equation.

225 - 25 = b^2.

200 = b^2. Take the square root of each side.

b = + / - 14.1 ft. Since - 14.1 ft is not an answer for a real dimension, the Answer is + 14.1 ft.

b) Now we need to reduce the 14.1 ft by 1 ft = 13.1 ft. The hypotenuse remains at 15 ft. We now need to find the new base, call it a. Same Pythagorean Theorem is used.

15^2 = a^2 + 13.1^2

225 = a^2 + 171.61. Subtract 171.61 from both sides.

225 - 171.61 = a^2

53.39 = a^2. Take the sq rt of each side.

a = 7.3 ft. Answer