Question

даны точки A(134;-887). B(133:-892), C(143:-890) найдите тангенс угла АВС

Answer 1

$BA=(134-133;-887+892)=(1;5)$
$|AB|= sqrt{1^2+5^2} = sqrt{26}$
$BC=(143-133;-890+892)=(10;2)$
$|BC|= sqrt{10^2+2^2}= sqrt{104}=2 sqrt{26}$
$cos(ABC)= frac{BA*BC}{|BA|*|BC|} = frac{1*10+5*2}{ sqrt{26}*2 sqrt{26} } = frac{20}{2*26} = frac{5}{13}$
$sin(ABC)= sqrt{1-cos^2(ABC)} = sqrt{1- frac{25}{169} } = sqrt{ frac{144}{169} } = frac{12}{13}$
$tg(ABC)= frac{sin(ABC)}{cos(ABC)} = frac{12}{13} : frac{5}{13} = frac{12}{5} =2,4$