в треугольнике АВС угол С=90 градусов,ВС=6см,cosA=0.8 найдите периметр треугольника

Решите задачу:

$cos\alpha=0,8\\\\sin^2\alpha+cos^2\alpha=1\\\\sin^2\alpha+0,8^2=1\\\\sin^2\alpha+0,64=1\\\\sin^2\alpha=1-0,64\\\\sin^2\alpha=0,36\\\\sin\alpha=\sqrt{0,36}\\\\sin\alpha=0,6$

$sin\alpha=\frac{|BC|}{|AB|}\\\\\frac{6}{|AB|}=0,6\\\\0,6|AB|=6\ \ \ \ /:0,6\\\\|AB|=10\ (cm)\\\\|BC|^2+|AC|^2=|AB|^2\\\\6^2+|AC|^2=10^2\\36+|AC|^2=100\\|AC|^2=100-36\\|AC|^2=64\\|AC|=\sqrt{64}\\|AC|=8\ (cm)$

$L=|AB|+|AC|+|BC|=10+8+6=24\ (cm)$