Question

Quanto valem os lados X e Y deste triângulo?

Answer 1

Vamos começar determinando o terceiro ângulo interno do triangulo.

Para isso vamos utilizar a soma dos ângulos internos:

$\theta~+~\alpha~+~\beta~=~180^\circ\\\\\\14^\circ~+~140^\circ~+~\beta~=~180^\circ\\\\\\\beta~=~180^\circ-14^\circ~-~140^\circ\\\\\\\boxed{\beta~=~26^\circ}$

Agora, utilizando a Lei dos Senos, podemos determinar "x" e "y":

$\frac{x}{sen(\beta)}~=~\frac{12}{sen(\alpha)}\\\\\\\frac{x}{sen(26^\circ)}~=~\frac{12}{sen(140^\circ)}\\\\\\\frac{x}{0,4384}~=~\frac{12}{0,6428}\\\\\\Multiplicando~Cruzado\\\\\\0,6428~.~x~=~12~.~0,4384\\\\\\x~=~\frac{5,2608}{0,6428}\\\\\\\boxed{x~\approx~8,18~cm}$

$\frac{y}{sen(\theta)}~=~\frac{12}{sen(\alpha)}\\\\\\\frac{y}{sen(14^\circ)}~=~\frac{12}{sen(140^\circ)}\\\\\\\frac{y}{0,2419}~=~\frac{12}{0,6428}\\\\\\Multiplicando~Cruzado\\\\\\0,6428~.~y~=~12~.~0,2419\\\\\\y~=~\frac{2,9028}{0,6428}\\\\\\\boxed{y~\approx~4,52~cm}$