Question

Obtenha o valor de sen (a + B)

Answer 1

$\large\boxed{\begin{array}{l}\rm vamos~achar~a~hipotenusa~do~tri\hat angulo~maior:\\\rm h^2=5^2+(2\sqrt{6})^2\\\rm h^2=25+24\\\rm h^2=49\\\rm h=\sqrt{49}\\\rm h=7\\\rm vamos~achar~o~cateto~do~tri\hat angulo~menor:\\\rm x^2+3^2=5^2\\\rm x^2+9=25\\\rm x^2=25-9\\\rm x^2=16\\\rm x=\sqrt{16}\\\rm x=4\end{array}}$

$\large\boxed{\begin{array}{l}\rm note~que:\\\rm sen(\alpha)=\dfrac{3}{5}~~cos(\alpha)=\dfrac{4}{5}\\\\\rm sen(\beta)=\dfrac{2\sqrt{6}}{7}~~cos(\beta)=\dfrac{5}{7}\\\\\rm sen( \alpha+\beta)=sen(\alpha)\cdot cos(\beta)+sen(\beta)\cdot cos(\alpha)\\\rm sen(\alpha+\beta)=\dfrac{3}{5}\cdot\dfrac{5}{7}+\dfrac{2\sqrt{6}}{7}\cdot\dfrac{4}{5}\end{array}}$

$\large\boxed{\begin{array}{l}\rm sen(\alpha+\beta)=\dfrac{15+8\sqrt{6}}{35}\end{array}}$