Question

determine o valor de x no triângulo ABC.
Com cálculos por favor.​

Answer 1

$\frac{ab}{ \sin(c) } = \frac{ac}{ \sin(b) } = \frac{bc}{ \sin(a) }$

$\frac{ \sqrt{93} }{ \sin(120) } = \frac{7}{ \sin(b) } = \frac{x}{ \sin(a) }$

$\frac{ \sqrt{93} }{ \sin(120) } = \frac{7}{ \sin(b) }$

$\frac{ \sqrt{93} }{0.87} = \frac{7}{ \sin(b) }$

$\sin(b) \times \sqrt{93} = 0.87 \times 7$

$\sin(b) \times 9.644 = 6.09$

$\sin(b) = 6.09 \div 9.644$

$\sin(b) = 0.63$

$b = 0.63 \times { \sin }^{ - 1}$

$b = 39$

A + B + C = 180 °

A + 39 + 120 = 180

A= 180 - 159

A= 21°

$\frac{7}{0.63} = \frac{x}{ \sin(21) }$

$\frac{7}{0.63} = \frac{x}{0.36}$

$0.63 \times x = 7 \times 0.36$

$0.63x = 2.52$

$x = 2.52 \div 0.63$

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$x = 4$

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