Question

В треугольнике ABC угол C = 90°, tgB = 4, AB=2√17. AC - ?

Answer 1

ΔABC, <C=90°, tgB=4, AC=2√17
AC=?

$1+ tg^{2} B= frac{1}{ cos^{2}B }$
$frac{1}{cos ^{2} B}=1+ 4^{2} , frac{1}{ cos^{2}B } =17$
$cos ^{2} B= frac{1}{17}$
$cosB= frac{1}{ sqrt{17} }$
$cosB= frac{CB}{AB} CB=AB*cosB CB=2$
$tgB= frac{AC}{CB} AC=CB*tgB AC=8$