Question

Razões Trigonométricas
Exercícios
1) Encontre os valores desconhecidos:

Answer 1

$\large\boxed{\begin{array}{l}\rm a)\\\sf sen(\alpha)=\dfrac{3}{5}\\\\\sf sen(\alpha)=0,6\\\sf \alpha=37^\circ\\\sf b)~\sf sen(\beta)=\dfrac{8}{10}\\\\\sf sen(\beta)=0,8\\\sf \beta=54^\circ\\\rm c)~\sf h=\sqrt{5^2+12^2}\\\sf h=\sqrt{25+144}\\\sf h=\sqrt{169}\\\sf h=13\\\sf sen(\alpha)=\dfrac{12}{13}=0,92\\\\\sf\alpha=67^\circ\\\sf \alpha+\beta=90^\circ\\\sf \beta=90^\circ-\alpha\\\sf \beta=90^\circ-67^\circ\\\sf\beta=23^\circ\end{array}}$

$\large\boxed{\begin{array}{l}\rm d)\\\sf tg(\alpha)=\dfrac{9}{12}\\\\\sf tg(\alpha)=0,75\\\sf \alpha=37^\circ\\\sf \beta=90^\circ-\alpha\\\sf \beta=90^\circ-37^\circ\\\sf\beta=53^\circ\\\rm e)~\sf tg(\alpha)=\dfrac{3}{4}=0,75\\\\\sf \alpha=37^\circ\\\rm f)~\sf tg(\beta)=\dfrac{25}{10}=2,5\\\sf\beta=68^\circ\\\sf \alpha=90^\circ-\beta\\\sf\alpha=90^\circ-68^\circ\\\sf\alpha=22^\circ\end{array}}$