Pythagorean Theorem - Examples, Exercises and Solutions

To find side AB, we will need to use the Pythagorean theorem.

The Pythagorean theorem allows us to find the third side of a right triangle, if we have the other two sides.

You can read all about the theorem here.

Pythagorean theorem:

$A^2+B^2=C^2$

That is, one side squared plus the second side squared equals the third side squared.

We replace the existing data:

$3^2+2^2=AB^2$

$9+4=AB^2$

$13=AB^2$

We find the root:

$\sqrt{13}=AB$

To find the length of the hypotenuse BC in a right-angled triangle where AB and AC are the other two sides, we use the Pythagorean theorem: $c^2 = a^2 + b^2$.

Here, $a = 6 \text{ cm}$ and $b = 8 \text{ cm}$.

Plugging the values into the Pythagorean theorem, we get:

$c^2 = 6^2 + 8^2$.

Calculating further:

$c^2 = 36 + 64$

$c^2 = 100$.

Taking the square root of both sides gives:

$c = 10 \text{ cm}$.

To solve the exercise, we have to use the Pythagorean theorem:

A²+B²=C²

We replace the data we have:

3²+4²=C²

9+16=C²

25=C²

5=C

We use the Pythagorean theorem

$AC^2+AB^2=BC^2$

We insert the known data:

$3^2+4^2=BC^2$

$9+16=BC^2$

$25=BC^2$

We extract the root:

$\sqrt{25}=BC$

$5=BC$

It is important to remember: the Pythagorean theorem is only valid for right-angled triangles.

This triangle does not have a right angle, and therefore, the missing side cannot be calculated in this way.