8,若△ABC的三边为a,b,c,它的面积为(a²+b²-c²)/4√3,那么内角∠C等于A30° B45° C60° D90°

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 19:03:13
8,若△ABC的三边为a,b,c,它的面积为(a²+b²-c²)/4√3,那么内角∠C等于A30° B45° C60° D90°

8,若△ABC的三边为a,b,c,它的面积为(a²+b²-c²)/4√3,那么内角∠C等于A30° B45° C60° D90°
8,若△ABC的三边为a,b,c,它的面积为(a²+b²-c²)/4√3,那么内角∠C等于
A30° B45° C60° D90°

8,若△ABC的三边为a,b,c,它的面积为(a²+b²-c²)/4√3,那么内角∠C等于A30° B45° C60° D90°
根据:余弦定理:c^2=a^2+b^2-2abcosC,∴a^2+b^2-c^2=2abcosC
S = 1/2absinC
S = (a^2+b^2-c^2)/4
1/2absinC= (a^2+b^2-c^2)/4 = 2abcosC/4√3
sinc/cosc=4/4√3
tanc=√3/3
c=30°
选A30°