What you’ll learn
Apply theorem to real situations.
Key idea
The ladder is opposite the right angle and is the hypotenuse; wall height and ground distance are legs.
Ladder is hypotenuse; physical leg lengths require positive root and feet units.
Worked example
Enter the exact value or ordered values in the format requested below.
A 100-foot ladder touches a vertical wall; base is 28 feet away on level ground. Find its wall height with unit.
- A vertical wall and level ground make a right triangle with ladder length 100 feet as hypotenuse.
- Height²=100²-28²=9216, giving height 96 feet; reversing known height gives base²=100²-96²=784, so base 28 feet.
Answer: 96 feet
Quick Check
Evaluate a worked attempt at apply theorem to real situations, identify the first invalid step, and provide the correction.
A 5-foot ladder stands 3 feet from vertical wall on level ground. Step 1 identifies ladder as hypotenuse. Step 2 subtracts lengths to report height 2 feet. Locate the first invalid step and correct the height.