If after reading the other pages and posts, you feel you need a brush-up on Pythagoras’ Theorem, read on.

We can see in the diagram below that, in the triangle ABC, if a perpendicular is dropped from point A to side a at point D, ABC is divided into 2 smaller triangles which are both similar to ABC.

Consider triangle (i). Since this triangle is similar to ABC, it follows that:

a÷b = b÷x

→ b^{2} = ax …………….(i)

Now consider triangle (ii); by similar argument:

a÷c = c÷y

→ c^{2} = ay …………….(ii)

Combining (i) and (ii) we get:

b^{2} + c^{2} = ax + ay

Þ a( x + y ) = b^{2} + c^{2}

But a = x + y

→ **a ^{2} = b^{2} + c^{2}** This is Pythagoras’ Theorem

** ****Simple Example**

The distance from town A to town B is 48.5Km.

The distance from town B to town C is 38.25Km.

What is the distance from town C to town A?

By Pythagoras,

CA^{2} = AB^{2} + BC^{2}

→ CA^{2} = 48.5^{2} + 38.25^{2}

= 2352.25 + 1463.06

= 3815.31

→ CA = √3815.31

= 61.77Km.

Therefore the distance from town C to town A is 61.77Km.

For more information: www.astronavigationdemystified.com

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