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Pythagorean theorem

In a right triangle, squared leg lengths sum to the squared hypotenuse length.

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Different ways to understand it

• Vector components: magnitude and direction

  Khan Academy · English · Application
  Connection evidence

  Reviewed English material v1: card "Magnitude from components using the Pythagorean theorem" at 4:19 — Because the components create a right triangle with the vector as hypotenuse, the magnitude is found from the sum of the squares of the components. Here $\|\vec{b}\|=\sqrt{(\sqrt{2})^2+(\sqrt{2})^2}=\sqrt{4}=2$. The board writes $\|\vec{b}\|=2$.

• Finding vector magnitude from components

  Khan Academy · English · Application
  Connection evidence

  Reviewed English material v1: card "Magnitude Formula via Pythagorean Theorem" at 0:26 — In orthonormal Cartesian coordinates, Euclidean length is the square root of the component squares. The perpendicular legs have lengths equal to the absolute component values. This formula does not apply unchanged to arbitrary nonorthogonal coordinates.

Knowledge connections

• Triangle similarity · Related · Map context
• Circle geometry · Related · Map context

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