Question

Considere o triângulo abaixo em que um dos ângulos mede 75° e o lado oposto a ele mede 90cm. Outro ângulo mede 80°. Calcule a medida do lado oposto ao ângulo de 80°. Dado: sen75=0,966; sen80=0,985. *

Answer 1

Utilizando a Lei dos Senos, temos:

$\sf \dfrac{x}{sen(80^\circ)}~=~\dfrac{90}{sen(75^\circ)}\\\\\\x~=~sen(80^\circ)\cdot\dfrac{90}{sen(75^\circ)}\\\\\\x~=~\dfrac{0,985\cdot 90}{0,966}\\\\\\x~=~\dfrac{985\cdot 90}{966}\\\\\\x~=~\dfrac{985\cdot 90}{966}~~~\Rightarrow~Simplificando~por~2\\\\\\x~=~\dfrac{985\cdot 45}{483}~~~\Rightarrow~Simplificando~por~3\\\\\\x~=~\dfrac{985\cdot 15}{161}\\\\\\x~=~\dfrac{14775}{161}\\\\\\\boxed{\sf x~=~\dfrac{14775}{161}~cm}~~ou~~ \boxed{\sf x~\approx~91,77~cm}$

$\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$