Pythagoras Theorem

Pythagoras Theorem is an important concept of trigonometry. Trigonometry means science which deals with the measurement of a triangle. Given two sides of a right angle triangle using Pythagoras theorem length of third side is easily determined.

A right triangle is one whose one angle is 90⁰ and the sum of the other two angles of is 90⁰. The longest side of right triangle is hypotenuse and is the side opposite to right angle.

 Pythagoras Theorem states that the sum of the squares of two sides of the right angle triangle is equal to the square of the hypotenuse.

Right Angle Triangle

In the figure given above triangle ABC (∆ABC- ∆ is symbol for triangle) angle ABC or angle B is 90⁰.

So AB²+ BC²= AC²

  AC=

When two sides of a right angle triangle are given it is very easy to find the third side.

Suppose in the given figure AB= 4, BC= 3 find AC=?

According to Pythagoras theorem AC²=  AB²+ BC²

        = 4²+ 3² =25

AC= sqrt( 25) =5

How we can use Pythagoras theorem?

1) Find the length of the diagonal of a rectangle whose sides are 5 and 12?

Find Length of diagonal AC

Each angle of a rectangle is 90⁰, in this sum two sides of rectangles are given. ∆ABC is a right angle triangle, with ∠ ABC/ ∠ B is 90⁰, so diagonal AC of rectangle is hypotenuse of ∆ ABC.

AC²= AB²+ BC²

          = 12²+ 5²

= 144+ 25 = 169

AC= sqrt(169 )= 13

AC=13

2) Find if a triangle with sides 17,14,8 is right angle triangle?

For a right angle triangle, sum of square of two sides = hypotenuse²
(hypotenuse is the longest side)

Let us check this theorem for the triangle with given sides 17, 14, 8

14²+ 8²= 196+ 64= 260

17²= 289

260 ≠ 289 the given triangle is not a right angle triangle.

<h3>Pythagorean Triple </h3>

A set of integer which follow Pythagoras theorem are Pythagorean Triple.

E.g. 1) 3, 4, 5

2) 5, 12, 13

3) 7, 24, 25

4) 8, 15, 17

5) 9, 40, 41