QUESTIO mono A15-1001 ladderisrestin wall. The height at which the top of the laddertouches the wall istwice the distance from the look of the ladder to thebaseofthewall. Find the distance (In feet) from the foot of the ladder to the base of the wall. coumber only (nounits)If youranswerisnotowhole number then round to the nearest hundredth. spoint Enter answer here...

## Step 1<br />The problem describes a right triangle, where the ladder acts as the hypotenuse, the height at which the ladder touches the wall is the opposite side, and the distance from the foot of the ladder to the base of the wall is the adjacent side.<br /><br />## Step 2<br />We are given that the height at which the ladder touches the wall is twice the distance from the foot of the ladder to the base of the wall. Let's denote the distance from the foot of the ladder to the base of the wall as \(x\). Therefore, the height at which the ladder touches the wall is \(2x\).<br /><br />## Step 3<br />We can apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the ladder, which is 15 feet long.<br /><br />### **The Pythagorean theorem: \(a^2 + b^2 = c^2\)**<br /><br />## Step 4<br />Substituting the given values into the Pythagorean theorem, we get:<br /><br />### **\(x^2 + (2x)^2 = 15^2\)**<br /><br />## Step 5<br />Solving this equation will give us the value of \(x\), which is the distance from the foot of the ladder to the base of the wall.