Latest Tweets

Free math worksheets

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.

In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

And it is valid in different order:

If the square of the hypotenuse is equal to the sum of the squares of the other two sides the triangle is a right angled.

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 the 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

If we have any other triangle, we can also use Pythagorean theorem.

If we have length of b and v_a, and a=12 we can find out other lengths in these triangle:

v_a=6cm

b=10cm

_______

c=?

b^2=v_a^2+x^2

x^2=b^2-v_a^2

x^2=100-36

x^2=64

x=8cm

Now, we can calculate:

a^2=v_a^2+y^2

y^2=a^2-v_a^2

y^2=144-36

y^2=108

y=\sqrt{108}

y=10.39cm

c=8+10.39

c=18.39 cm

Pythagorean theorem worksheets

Right triangle

  Integers (181.1 KiB, 303 hits)

  Decimals (190.9 KiB, 245 hits)

  Radicals (467.3 KiB, 269 hits)

  Triangle area (139.6 KiB, 294 hits)

Specials

  Special right triangles (389.8 KiB, 339 hits)

  Multi-step triangle problems (175.1 KiB, 293 hits)

Shares