triangulo retangul (G1 1996 ) O valor de a e c no trangulo ABC é:

30 graus , cateto oposto 18 , cateto adjacente c , hipotenusa a

Resposta :

[tex]\sin30^{\circ}=\dfrac{18}{a}\Longrightarrow\dfrac{1}{2}=\dfrac{18}{a}\Longrightarrow\boxed{a=36}\\\\\\ \tan30^{\circ}=\dfrac{18}{c}\Longrightarrow\dfrac{\sqrt{3}}{3}=\dfrac{18}{c}\Longrightarrow c=\dfrac{18\cdot3}{\sqrt{3}}=\dfrac{18\cdot3}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}\Longrightarrow\boxed{c=18\sqrt{3}}[/tex]
Valor a=
seno de 30= 18/x
1/2=18/x
x=36  Hipotenusa igual a 36.

Cosseno de 30=x/36
[tex] \sqrt{3}/2[/tex]=x=36
2x=36[tex] \sqrt{3} [/tex]
x=36[tex] \sqrt{3} [/tex]/2
x=18[tex] \sqrt{3} [/tex]

Valor da hipotenusa é 36 e do cat. adjacente é 18[tex] \sqrt{3} [/tex]

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