Question

Qual é o ângulo agudo a, formado entre as retas r: y = 1/3 x + 2 e s: y = - 1/2 x + 6?

A 35°
B 45°
C 90°
D 60°

Alguém me ajuda ae, por favor

Answer 1

$r: y=\frac{1}{3}x+2$  ⇒  $m_{r}=\frac{1}{3}$

$s:y=-\frac{1}{2}x+6$  ⇒  $m_{s}=-\frac{1}{2}$

$tg\alpha =|\frac{m_{s}-m_{r}}{1+m_{s}.m_{r}}|\\\\tg\alpha =|\frac{(-\frac{1}{2})-(\frac{1}{3})}{1+(-\frac{1}{2}).(\frac{1}{3})}|\\\\tg\alpha =|\frac{-\frac{1}{2}-\frac{1}{3}}{1-\frac{1}{6}}|\\\\tg\alpha =|\frac{-\frac{5}{6}}{\frac{5}{6}}|\\\\tg\alpha =|-1|\\\\tg\alpha =1\\\\\alpha =45^{0}$