Question

Área de triângulo sem altura!

Sabendo que:
b = c + 1,34 m; c = 2b - 11,34 m e α = 30° calcule a área do triângulo abc (imagem em anexo), utilizando o método de Bèzout. Calcule o valor de "a".

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Answer 1

Resposta:

A = 21,79 m²

Explicação passo a passo:

b = c + 1,34  e  c = 2b - 11,34

c = 2(c + 1,34) - 11,34

c = 2c + 2,68 - 11,34

c - 2c =  - 8,69

-c = -8,69

c = 8,68

b = 8,69 + 1,34

b = 10,03 m

$A=\frac{bc}{2}*sen\alpha \\\\A=\frac{10,03*8,69}{2} *sen30\°\\\\A=43,58035 *0,5\\\\A=21,79 m\²$

Answer 2

$\boxed{\begin{array}{l}\sf b=c+1,34~~c=2b-11,34\\\begin{cases}\sf b=c+1,34\\\sf c=2b-11,34\end{cases}\\\sf substituindo\,a\,2^a~equac_{\!\!,}\tilde ao\,na\,1^a\,temos:\\\sf b=2b-11,34+1,34\\\sf b-2b=-10\\\sf -b=-10\cdot (-1)\\\sf b=10\,m\\\sf c=2b-11,34\\\sf c=2\cdot10-11,34\\\sf c=20-11,34\\\sf c=8,66\,m\end{array}}$

$\boxed{\begin{array}{l}\sf pela\,lei\,dos\,cossenos\,podemos\,escrever:\\\sf a^2=10^2+8,66^2-2\cdot10\cdot8,66\cdot cos(30^\circ)\\\sf a^2=100+74,99-\diagup\!\!\!2\cdot10\cdot8,66\cdot\dfrac{\sqrt{3}}{\diagup\!\!\!2}\\\\\sf a^2=174,99-149,99\\\sf a^2=25\\\sf a=\sqrt{25}\\\\\sf a=5\,m\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf \acute Area\,do\,tri\hat angulo\,em\,func_{\!\!,}\tilde ao\,dos\,lados}\\\underline{\sf e\,do\,\hat angulo\,entre\,eles}\\\sf A=\dfrac{1}{2}\cdot b\cdot c\,sen(\alpha)\end{array}}$

$\boxed{\begin{array}{l}\sf A=\dfrac{1}{2}\cdot10\cdot8,66\cdot sen (30^\circ)\\\\\sf A=\dfrac{1}{2}\cdot10\cdot 8,66\cdot\dfrac{1}{2}\\\\\sf A=\dfrac{86,6}{4}\\\\\sf A=21,65\,m^2\end{array}}$