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Natasha2012 [34]
3 years ago
11

Can i use the pythagorythm therom on all triangles

Mathematics
2 answers:
Umnica [9.8K]3 years ago
5 0
No, you can only use the Pythagorean theorem on right triangles. 
LenKa [72]3 years ago
5 0
Pythagoreans' theorem only applies to right angle triangles.

To find unknowns of an irregular triangle use

a² = b² + c² -2bc cos A
( for length and angle )

and

½ ab sin C ( for area )
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\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)

Factorize the left side.

2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)

Pythagorean identity:

\cos^2(x) + \sin^2(x) = 1

\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)

so that

\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}

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