Question

O angulo agudo de (alfa) de um triangulo retangulo e tal que sen alfa=0,6.Podemos,entao afirmar que: cos alfa=___ e tang alfa =____ ?

Answer 1

$sen~\alpha=0,6\\sen~\alpha=6/10\\sen~\alpha=3/5$

$sen^{2}\alpha+cos^{2}\alpha=1\\cos^{2}\alpha=1-sen^{2}\alpha\\cos^{2}\alpha=1-(3/5)^{2}\\cos^{2}\alpha=1-(9/25)\\cos^{2}\alpha=(25/25)-(9/25)\\cos^{2}\alpha=(25-9)/25\\cos^{2}\alpha=16/25\\cos~\alpha=\sqrt{16/25}\\cos~\alpha=4/5\\cos~{\alpha}=0,8$

$tg~\alpha=sen~\alpha/cos~\alpha\\tg~\alpha=(3/5)/(4/5)\\tg~\alpha=(3/5)*5/4\\tg~\alpha=3/4\\tg~\alpha=0,75$