Question

Observe a figura abaixo e calcule o valor da medida X.

a) 140,21

b) 141,32

c) 141,42

d) 142,13​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm o~3^o~\hat angulo~mede}\\\sf 180^\circ-150^\circ=30^\circ\\\underline{\rm Pela~lei~dos~senos~temos:}\\\sf\dfrac{x}{sen(45^\circ)}=\dfrac{100}{sen(30^\circ)}\\\\\sf x\cdot sen(30^\circ)=100\cdot sen(45^\circ)\\\sf x\cdot\dfrac{1}{\backslash\!\!\!2}=100\cdot\dfrac{\sqrt{2}}{\backslash\!\!\!2}\\\sf x=100\sqrt{2}\\\underline{\rm adotando~\sqrt{2}=1,4142~temos:}\\\sf x=100\cdot1,4142=141,42\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$