Pythagoras Theorem.

What is the rule for Pythagorean theorem?

What is the Pythagoras Theorem in Math? The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.

When given two sites of a right-angle triangle, we use Pythagoras theorem to solve for the unknown (third) side.

Where the longest side “c” is known as the Hypotenuse side, the Base side “b” is known as the Adjacent side and the Altitude “a” is known as the opposite side.

Example:
Find the side labeled x in the fig.1 given below:







Solution

Fig. 1 is a right-angle triangle with two sides known and 1 side unknown. We are required to solve for the unknown side labeled x. Hence, we use Pythagoras' theorem as it perfectly describes the problem at hand.
But Pythagoras states Mathematically that:
|CB|2 = |AB|2 + |AC|2
We were given:
|CB| = xcm
|AB| = 5cm
|AC| = 4cm

Next, we slot the given values into the formula as follows:
x2 = 52 + 42
x2 = 25 + 16
x2 = 41

Taking the square root of both sides, we have
   =  

x = 6.4cm