Question

sin^2a+sin^2b=sin^2c 则△ABC为

直角/等腰直角/等边/等腰？

Answer 1

(sina)²+(sinb)²=(sinc)²
=[sin(180°-a-b)]²
=[sin(a+b)]²
=(sinacosb+cosasinb)²
(sina)²+(sinb)²=(sina)²(cosb)²+(cosa)²(sinb)²
(sina)²(cosb)²+(cosa)²(sinb)²-(sina)²-(sinb)²=0
(sina)²[(cosb)²-1]+(sinb)²[(cosa)²-1]=0
(sina)²(sinb)²=0
sina=0或sinb=0
a=90°或b=90°
三角形为直角三角形。