Question

в треугольнике ABC угол C равен 90, CH-высота ,AC=10, tgA=корень из 21/2.найдите AH

Answer 1

$tgA= frac{CB}{AC}$
$frac{ sqrt{21} }{2}=frac{CB}{10}$
$CB=5 sqrt{21}$
$AB= sqrt{AC^{2}+CB^{2}}= sqrt{100+25*21}= sqrt{625}=25$
$CH= frac{AC*CB}{AB}= frac{10*5 sqrt{21}}{25}=2sqrt{21}$
$AH= sqrt{AC^{2}- CH^{2}}= sqrt{100-4*21}=4$