Question

Найти угол между прямыми 2x-y+1=0 и x+4y-5=0

Answer 1

$2x-y+1=0\Rightarrow y=2x+1\\x+4y-5=0\Rightarrow y=-\frac14x+\frac54\\\\k_1=2,\;k_2=-\frac14\\\\tg\gamma=\left|\frac{k_1-k_2}{1+k_1\cdot k_2}\right|=\left|\frac{2+\frac14}{1-\frac12}\right|=\left|\frac{\frac94}{\frac12}\right|=\left|\frac{18}4\right|=4,5\\\\\gamma=arctg(4,5)$