Question

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

Answer 1

cosA=0.8

cosA= AC/AB

$sinA= sqrt{1-cos^2A} = sqrt{1-0.64}= sqrt{0.36} =0.6$

sinA=BC/AB

AB=BC/sinA=6/0.6=10

AC=AB*cosA=10*0.8=8

P=6+10+8=24 см

Answer 2

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

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


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