Question

qual a área de uma região triangular que tem lados de 10 cm e 30 cm e entre esses lados um ângulo de 30°?​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf \acute Area~do~tri\hat angulo~em~func_{\!\!,}\tilde ao~dos~lados}\\\underline{\sf e~do~\hat angulo~compreendido~entre~eles.}\\\rm Sejam~a~e~b~os~lados~de~um~tri\hat angulo~qualquer\\\rm e~\theta~o~\hat angulo~compreendido~entre~a~e~b.\\\rm A~\acute area~deste~tri\hat angulo~\acute e~dada~por\\\rm A=\dfrac{a\cdot b\cdot sen(\theta)}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\sf dados:\begin{cases}\sf a=10\,cm\\\sf b=30\,cm\\\sf \theta=30^\circ\\\rm A=?\end{cases}\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm A=\dfrac{a\cdot b\cdot sen(\theta)}{2}\\\\\rm A=\dfrac{10\cdot30\cdot sen(30^\circ)}{2}\\\\\rm A=\dfrac{300sen(30^\circ)}{2}\\\\\rm A=150\cdot sen(30^\circ)\\\rm A=150\cdot \dfrac{1}{2}\\\\\rm A=\dfrac{150}{2}\\\\\rm A=75\,cm^2\end{array}}$