Question

A farmer leans a 12-ft ladder against a barn. The base of the ladder is 3 ft from the barn. To the nearest tenth, how high on the barn does the ladder reach?

Answer 1

The barn, the ground, and the ladder form a right triangle. If we represent the height on the barn by y, then the Pythagorean theorem tells us

... hypotenuse² = (side1)² + (side2)²

... (12 ft)² = (3 ft)² + y² . . . . . . . . . . . . fill in given information

... 144 ft² - 9 ft² = y² = 135 ft² . . . . . .subtract (3 ft)²

... y = 3√15 ft ≈ 11.6 ft . . . . . . . . . . . take the square root

The ladder reaches 11.6 feet high on the barn.

Answer 2

You have to use the Pithagorean Theorem because the ladder, the barn and the earth forms triangle. Than the wall of the barn and the earth makes a 90° angle. So the ladder is the hypotenuses and the earth and the barn wall are the catetes so you only have to do 12^2= 3^2 + x^2. x is how high on the barn the ladder reach. That's all. I hope I helped.