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Re: [obm-l] trigonometria
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] trigonometria
- From: "Renan Kruchelski Machado" <renankmachado@xxxxxxxxx>
- Date: Tue, 27 Mar 2007 00:21:06 -0300
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1) Por que o triangulo tem que ser retangulo??
senA + senB + senC = 2*sen(A+B)/2*cos(A-B)/2 + 2*sen(A+B)/2*cos(A+B)/2 =
2*sen(A+B)/2 ( cos(A-B)/2 + cos(A+B)/2) = 2*cosC/2 ( 2*cosA/2*cosB/2) =
4*cosA/2*cosB/2*cosC/2.
Eu nao usei em nenhuma parte que ele tem que ser retangulo.
Em 26/03/07, Julio Sousa <juliosousajr@gmail.com
> escreveu:
1) Sendo A, B, C ângulos internos de um triângulo retângulo, prove que:
senA + senB + senC = 4*cos(A/2)*cos(B/2)*cos(C/2)
2) Se num triângulo retângulo for satisfeita a igualdade cosB = senA/2*senC, existirá entre seus ângulos a relação
a) B = A+C
b) B = 2C
c) C = 2B
d) C = A - B
e) B = C
--
Atenciosamente
Júlio Sousa