Question

pfv gente
Determine a medida de x e y em cada caso​

Answer 1

Explicação passo-a-passo:

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a) Temos em relação ao ângulo de 60°:

$\text{cateto oposto = 4}\\\text{cateto adjacente = y}\\\text{hipotenusa = x}$

Calculando o valor de x:

$sen\ 60^{\circ} =\dfrac{\text{cateto oposto }}{\text{hipotenusa}}\\\\\dfrac{\sqrt{3} }{2}=\dfrac{4}{x}\\\\\sqrt{3} . x =4.2\\\\x=\dfrac{8}{\sqrt{3} }.\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\boxed{x=\dfrac{8.\sqrt{3}}{3}}$

Calculando o valor de y:

$tg\ 60^{\circ} =\dfrac{\text{cateto oposto}}{\text{cateto adjacente}} \\\\\sqrt{3} =\dfrac{4}{y}\\\\y=\dfrac{4}{\sqrt{3} } .\dfrac{\sqrt{3}}{\sqrt{3}} \\\\\boxed{y=\dfrac{4.\sqrt{3}}{3}}$

b) Temos em relação ao ângulo de 45°:

$\text{cateto oposto = x}\\\text{cateto adjacente = y}\\\text{hipotenusa = }7\sqrt{2}$

Calculando o valor de x:

$sen\ 45^{\circ} =\dfrac{\text{cateto oposto}}{\text{hipotenusa}} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{x}{7\sqrt{2} } \\\\2.x=7.\sqrt{2} .\sqrt{2} \\\\2x=7.2\\\\2x=14\\\\x=\dfrac{14}{2} \\\\\boxed{x=7}$

Calculando o valor de y:

$cos\ 45^{\circ} =\dfrac{\text{cateto adjacente}}{\text{hipotenusa}} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{y}{7\sqrt{2} } \\\\2.y=7.\sqrt{2} .\sqrt{2} \\\\2y=7.2\\\\2y=14\\\\y=\dfrac{14}{2} \\\\\boxed{y=7}$