Question

Determine o valor de x nos triângulos abaixo

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf x\cdot sen(30^\circ)=5\cdot sen(45^\circ)\\\sf x\cdot\dfrac{1}{\backslash\!\!\!2}=5\cdot\dfrac{\sqrt{2}}{\backslash\!\!\!2}\\\sf x=5\sqrt{2}~cm\\\tt b)~\sf x^2=7^2+5^2-2\cdot7\cdot5\cdot cos(30^\circ)\\\sf x^2=49+25-\backslash\!\!\!2\cdot7\cdot5\cdot\dfrac{\sqrt{3}}{\backslash\!\!\!2}\\\sf x^2=74-35\sqrt{3}\\\sf x=\sqrt{74-35\sqrt{3}}\end{array}}$