Question

Lei dos cossenos. Trigonometria. Se alguém puder ajudar agradeço. Resposta: a)= 0.5. Por favor!!

Answer 1

$a^2=b^2+c^2-2bc\cdot cos\left(A\right)\\\left(\sqrt{19}\right)^2=2^2+5^2-2\cdot 2\cdot 5\cdot cos\left(\alpha \right)\\19=4+25-20\cdot cos\left(\alpha \right)\\19=29-20\cdot cos\left(\alpha \right)\\19-29=-20\cdot cos\left(\alpha \right)\\-10=-20\cdot cos\left(\alpha \right)\\cos\left(\alpha \right)\cdot 20=10\\cos\left(\alpha \right)=\frac{10}{20}\\cos\left(\alpha \right)=0,5\\Arccos\left(\alpha \right)=60^\circ\\\\\boxed{\boxed{\bold{cos\alpha =0,5}}}$