Question

Calcule X e Y
imagem Abaixo

Answer 1

$\boxed{\boxed{sen(\theta)= \frac{\text{Cateto oposto ao angulo }\theta}{hipotenusa} }}\\\\\\\boxed{\boxed{cos(\theta)= \frac{\text{Cateto adjascente ao angulo }\theta}{hipotenusa} }}$

a) 

$sen(30)= \frac{y}{6}\\\\ \frac{1}{2}= \frac{y}{6}\\\\ \frac{1}{2}*6 = y\\\\\boxed{3=y }$

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$sen(30)= \frac{x}{6+4} \\\\ \frac{1}{2}= \frac{x}{10} \\\\\boxed{ 5=x}$

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b)

$sen(60) = \frac{x}{6} \\\\ \frac{\sqrt{3}}{2} = \frac{x}{6} \\\\ \frac{\sqrt{3}}{2} *6= x\\\\ \boxed{3\sqrt{3}=x}$

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$cos(60)= \frac{y}{6}\\\\ \frac{1}{2}= \frac{y}{6}\\\\\boxed{3=y}$

Answer 2

Aplicando relações trigonométricas

1)
           $\frac{y}{6} =sen30 \\ \\ y=6sen30 \\ \\ sen30=0,5 \\ \\ y=6x(0,5) \\ \\ y=3$

           $\frac{x}{6+4} =sen30 \\ \\ x=10sen30 \\ \\ x=10x(0,5) \\ \\ x=5$

2)
           $\frac{x}{6} =sen60 \\ \\ x=6sen60 \\ \\ sen60=0,8660 \\ \\ x=6x(0,8660) \\ \\ x=6,196 \\ \\ x=1,2$

           $\frac{y}{6} =cos60 \\ \\ y=6cos60 \\ \\ cos60=0,5 \\ \\ y=6x(0,5) \\ \\ y=3$