Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
In plain words: Students use a² + b² = c² to find unknown side lengths of right triangles in real-world and math problems, in two and three dimensions.
Quick picks
Example problem- Assign problem on Goblins →A ‑foot ladder leans against a vertical wall. The base of the ladder is feet from the wall.
How high up the wall does the ladder reach? - Common mistake
- Adding when you need to subtract: with a leg of 5 and a hypotenuse of 13, the other leg is √(13² − 5²) = 12, not √(13² + 5²) ≈ 13.9.
Example Problems
A ‑foot ladder leans against a vertical wall. The base of the ladder is feet from the wall.
How high up the wall does the ladder reach?
How high up the wall does the ladder reach?
A square tile measures 15 centimeters on each side.
What is the diagonal distance across the tile?
Write your answer as a decimal rounded to the nearest hundredth.
What is the diagonal distance across the tile?
Write your answer as a decimal rounded to the nearest hundredth.
Aria runs 5 miles east and then a certain number of miles north.
She ends 13 miles away from her starting position.
How many miles north did Aria run?
She ends 13 miles away from her starting position.
How many miles north did Aria run?
Khan Academy ResourcesPythagorean theorem intro problemsUse Pythagorean theorem to find right triangle side lengthsUse Pythagorean theorem to find isosceles triangle side lengthsPythagorean theorem in 3DUse Pythagorean theorem to find areaUse Pythagorean theorem to find perimeterUse area of squares to visualize Pythagorean theoremRight triangle side lengthsPythagorean theorem word problemsIntro to the Pythagorean theorem 2Intro to the Pythagorean theoremPythagorean theorem word problem: carpetPythagorean theorem word problem: fishing boatPythagorean theorem examplePythagorean theorem in 3D
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