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
→ b2 = ax …………….(i)
Now consider triangle (ii); by similar argument:
a÷c = c÷y
→ c2 = ay …………….(ii)
Combining (i) and (ii) we get:
b2 + c2 = ax + ay
Þ a( x + y ) = b2 + c2
But a = x + y
→ a2 = b2 + c2 This is Pythagoras’ Theorem
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?
CA2 = AB2 + BC2
→ CA2 = 48.52 + 38.252
= 2352.25 + 1463.06
→ CA = √3815.31
Therefore the distance from town C to town A is 61.77Km.
For more information: www.astronavigationdemystified.com