Lesson 6 Homework Practice Use The Pythagorean Theorem Apr 2026

She spread the blueprint across the kitchen table. The lantern room (Point A) was 40 feet above the rocky ground (Point B). The base of the cliff (Point C) was 30 feet away from the lighthouse door because of a jagged drop-off.

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."

"If I put the ladder straight down from A to B," Sarah murmured, "it's 40 feet. But the ground slopes away. The building code says the ladder’s foot must rest on stable ground at Point C, 30 horizontal feet from the lighthouse wall." Lesson 6 Homework Practice Use The Pythagorean Theorem

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)

Most kids measured TV screens or ladder heights. But Sarah’s Nonna had just bought the lighthouse at auction. "It’s a fixer-upper," her grandmother had said, handing Sarah a dusty floor plan. "But the old spiral staircase is gone. We need to install a new fire escape ladder from the lantern room to the ground." She spread the blueprint across the kitchen table

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."

That’s when Sarah saw it—a perfect right triangle. The next day in class, Mr

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

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.

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

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