Aladder is leaning against a wall. the top of the ladder is 999 feet (\text{ft})(ft)left parenthesis, f, t, right parenthesis above the ground. if the bottom of the ladder is moved 3\,\text{ft}3ft3, space, f, t farther from the wall, the ladder will be lying flat on the ground, still touching the wall. how long, in feet, is the ladder?

The ladder is 166335 feet long. For this problem, we have a right triangle. The hypotenuse is the length of the ladder. The short leg is 999 feet long and the long leg is the length of the hypotenuse - 3. So let's make an equation to express this knowledge. 999^2 + (h-3)^2 = h^2 Expand expression 999^2 + h^2 - 6h + 9 = h^2 Subtract h^2 from both sides 999^2 -6h + 9 = 0 Add 6h to both sides 999^2 + 9 = 6h Do the squaring and adding. 998010 = 6h Divide both sides by 6 166335 = h So the ladder is 166335 feet long.