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How to use the Pythagorean theorem?

right triangles

Pythagorean theorem

The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse c.

We can imagine something like this:

pythagorean theorem

Image credit: Wikimedia Commons user AmericanXplorer13

 

Egyptian triangle

The right Triangle whose length of sides is equal to 3, 4 and 5 is called the Egyptian triangle.

Let’s forget that we know that the length of hypotenuse is equal to 5 and try to calculate it using Pythagorean theorem.

We have:

egyptian triangle

\ c^2 = a^2 + b^2

Where a = 4, and b = 3.

c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25
c=5

If we know lengths of any two sides of a right triangle, we can use this theorem to quickly find third.

egyptian triangle task

c^2 = a^2 + b^2

Where c = 10, and b = 83.

a^2 = c^2 - b^2
a^2 = 100 - 64
a^2 = 36
a = 6

 

Pythagorean theorem worksheets

Right triangle

  Integers (181.1 KiB, 264 hits)

  Decimals (190.9 KiB, 234 hits)

  Radicals (467.3 KiB, 251 hits)

  Triangle area (139.6 KiB, 255 hits)

Specials

  Special right triangles (389.8 KiB, 297 hits)

  Multi-step triangle problems (175.1 KiB, 254 hits)

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