Chain of reasoning for the hypotenuse (1 Viewer)

[Flairs]

Hi Everyone.

Just need a little help if there is anyone willing. The question reads: The hypotenuse is always called the longest side in a right-angled triangle. Can you explain why it is through a chain of reasoning.

I know Pythagoras theorem and how to work it out but dont know how to explain the above question through a chain of reasoning.


Can anyone help please? Any help would be greatly apprecicated.

Thanks

 

[foram]

Hi Everyone.

Just need a little help if there is anyone willing. The question reads: The hypotenuse is always called the longest side in a right-angled triangle. Can you explain why it is through a chain of reasoning.

I know Pythagoras theorem and how to work it out but dont know how to explain the above question through a chain of reasoning.


Can anyone help please? Any help would be greatly apprecicated.

Thanks

Pythagoras Theorem;
a^2 + b^2 = c^2

We note that;
a^2 > 0
b^2 > 0

[the square of a real number is always positive]

therefore,
c^2 > a^2
c^2 > b^2

meaning, c is the longest side.

 

[lyounamu]

Hi Everyone.

Just need a little help if there is anyone willing. The question reads: The hypotenuse is always called the longest side in a right-angled triangle. Can you explain why it is through a chain of reasoning.

I know Pythagoras theorem and how to work it out but dont know how to explain the above question through a chain of reasoning.


Can anyone help please? Any help would be greatly apprecicated.

Thanks

I don't know what you mean by chain of reasoning. But here we go:
Let h = hypotenuse
a = adjacent side
o = opposite side

All of h, a and o are positive as they indicate lengths.


Using cos rule: h^2 = a^2 + b^2 - 2ab cos(90)
= a^2 + b^2
And this is same as the Pythagoras' theorem which shows that the hypotenuse is always the longest side in a right-angled triangle.