三角形ABC的对边为abc.已知A-B=90°,a加b=根号2b,求∠C?
问题描述:
三角形ABC的对边为abc.已知A-B=90°,a加b=根号2b,求∠C?
答
当a+c=√2b.根据正弦定理有:sinA+sinC=√2sinB,sinA+sinC=√2sin[π-(A+C)]∵A-C=90°∴sin(90°+C)+sinC=√2sin[(90°+C)+C]cosC+sinC=√2sin(90°+2C),cosC+sinC=√2cos2C,cosC+sinC=√2(cos^2C-sin^2C)cosC+sinC...