Question

Rt△ABC的斜边AB在平面α内,直角顶点C在α内的射影为C′,则△ABC′是(    )

A.直角三角形                                   B.锐角三角形

C.钝角三角形                                   D.锐角或钝角三角形

Answer 1

答案:C

解析:由题知AC²＞AC′²,BC²＞BC′²,

又AC²+BC²=AB²,∴AC′²+BC′²＜AB².

由余弦定理,有cos∠AC′B=,

即∠AC′B为钝角.故△ABC′是钝角三角形.