Lesson 6 — Homework Practice Use The Pythagorean Theorem

She checked her work twice. Then she sketched the right triangle on her homework paper, labeling the legs and hypotenuse. Under "Practice," she wrote: A 40-ft height and a 30-ft horizontal distance create a 50-ft ladder. The Pythagorean theorem proves it works.

"Fifty feet," she whispered. "The ladder needs to be fifty feet long."

The next day in class, Mr. Elian held up Sarah’s homework. "This is what I wanted," he said. "You didn't just plug numbers into a formula. You found the hidden right triangle in a real place." Lesson 6 Homework Practice Use The Pythagorean Theorem

That night, Nonna called a contractor. "Fifty feet," she told him firmly. "My granddaughter did the math."

Her pencil moved to the margin of the homework sheet. Lesson 6: The Pythagorean Theorem. a² + b² = c². She checked her work twice

The old lighthouse on Breaker Point had been silent for forty years, but Sarah’s geometry teacher, Mr. Elian, had given her class an unusual challenge: "Use the Pythagorean Theorem to solve a real problem, or create one."

Sarah smiled, looking out the window toward the sea. The lighthouse’s new ladder would lean exactly 50 feet—no more, no less. And forty years of silence would end with the sound of safe, steady footsteps climbing up into the light. If the contractor only had a 45-foot ladder, how much closer to the lighthouse would the base have to be to still reach the lantern room? (Answer: 20.6 ft away, using 45² – 40² = b² → b ≈ 20.6 ft) The Pythagorean theorem proves it works

That’s when Sarah saw it—a perfect right triangle.