A ladder against a vertical wall forms a right triangle with the ground. The ladder is the hypotenuse, the side across from the right angle, so the height must be shorter than the ladder. Look for a scaled -- triangle before doing arithmetic. Subtracting the two given lengths does not give the height.
Hints
- Hint 1
The wall and ground meet at a right angle. The hypotenuse is the side across from that angle and is the longest side. Which part of this problem is the hypotenuse?
- Hint 2
A -- Pythagorean triple gives the sides of a right triangle. Compare the longest side with the ladder and the shortest side with the base distance. What factor scales both?
Step-by-step
Use a scaled right triangle
Step 1Identify the longest side
No Desmos needed. These lengths fit a scaled -- right triangle. The vertical wall meets the ground at a right angle, so the wall, ground, and ladder form a right triangle. The ladder is the hypotenuse, the side across from that angle. Its 15-foot length is the longest side.
- Step 2
Match the given lengths to a pattern
The sides of a -- right triangle can all be multiplied by the same number to make a larger triangle. Compare its shortest and longest sides with the given lengths: . So both given lengths are three times the matching sides of that triangle.
- Step 3
Scale the remaining side
The height matches the remaining side, . Scale it by : . So the top of the ladder touches the wall 12 feet above the ground. Choice B.