Question

e) Nesse item, calcule x.

Answer 1

Resposta:

Explicação passo a passo:

No triângulo mais à esquerda

$tg\alpha =\frac{2}{4} == > tg\alpha =\frac{1}{2}$

Relação trigonométrica com soma de ângulos

$tg2\alpha =\frac{2tg\alpha }{1-tg^22\alpha } \\\\tg2\alpha =\frac{2*\frac{1}{2} }{1-(\frac{1}{2} )^2}\\\\tg2\alpha =\frac{1 }{1-\frac{1}{4} }\\\\tg2\alpha =\frac{1 }{\frac{3}{4} }\\\\tg2\alpha =\frac{4}{3}$

No triângulo ABC

$tg2\alpha =\frac{2+x}{4} \\\\\frac{4}{3} =\frac{2+x}{4}\\\\3*(2+x)=4*4\\\\6+3x = 16\\\\3x=16-6\\\\3x = 10\\\\x=\frac{10}{3}$