Question

1) determine o valor de x em cada caso.

Answer 1

A)

$cosseno(30°) = \frac{16}{x} \\ \\ cosseno(30°) \times x = \frac{16}{x} \times x \\ \\ x \times cosseno(30°) = 16 \\ \\ x \times \frac{ \sqrt{3} }{2} = 16 \\ \\ x \times \frac{ \sqrt{3} }{2} \times 2 = 16 \times 2 \\ \\ x \sqrt{3} = 32 \\ \\ \frac{x \sqrt{3} }{ \sqrt{3} } = \frac{32}{ \sqrt{3} } \\ \\ x = \frac{32}{ \sqrt{ 3} }$

B)

$seno(x) = \frac{13}{26} \\ \\ arco \: seno(seno(x)) = arco \: seno( \frac{13}{26} ) \\ \\ x = 30° \\ \\ \\ observe \: que \: \frac{13}{26} = \frac{1}{2}$

C)

$seno(60°) = \frac{x}{18} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{18} \\ \\ 2x = 18 \sqrt{3} \\ \\ x = \frac{18 \sqrt{3} }{2} \\ \\ x = 9 \sqrt{3}$

D)

$cosseno(45°) = \frac{20}{x} \\ \\ \frac{ \sqrt{2} }{2} = \frac{20}{x} \\ \\ x \sqrt{2} = 40 \\ \\ x = \frac{40}{ \sqrt{2} }$