Question

na figura a seguir determine a medida do segmento AB, em cm, sabendo que seno de a=0,6​

Answer 1

$\large\boxed{\begin{array}{l}\rm Veja\,a\,figura\,que\,eu\,anexei.\\\rm note~que~pelo~teorema~do~\hat angulo~externo\\\rm \theta=2a.\\\rm vamos~descobrir~quanto~vale~sen(2a)\\\rm para~descobrir~AB.\\\rm sen(a)=0,6\longrightarrow sen^2(a)=0,36\\\rm cos^2(a)=1-0,36=0,64\\\rm cos(a)=\sqrt{0,64}=0,8\\\rm sen(2a)=2\cdot sen(a)\cdot cos(a)\\\rm sen(2a)=2\cdot0,6\cdot0,8\\\rm sen(2a)=0,96\\\rm sen(2a)=\dfrac{AB}{100}\\\\\rm AB=100\cdot sen(2a)\\\rm AB=100\cdot0,96\\\rm AB=96~cm\end{array}}$