作业帮高一数学,正弦定理第9题
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/25 07:36:16
高一数学,正弦定理第9题
解析：本题考查知识点：正弦定理,两角和与差的正弦由正弦定理a/sinA = b/sinB = 2R知：a = 2RsinA,b = 2RsinB
∵C=60°∴A+B = 120°,∴B=120°-A∴(a+b)/R = (2RsinA+2RsinB)/R
= 2R(sinA + sinB)/R= 2(sinA+sinB)=2[sinA+sin(120°-A)]=2(sinA+sin120°cosA-cos120sinA)=2(sinA+√3/2cosA+1/2sinA)=2(3/2sinA+√3/2cosA)=2√3(√3/2 sinA+1/2 cosA)=2√3sin(A+60°)∵0
∵C=60°∴A+B = 120°,∴B=120°-A∴(a+b)/R = (2RsinA+2RsinB)/R
= 2R(sinA + sinB)/R= 2(sinA+sinB)=2[sinA+sin(120°-A)]=2(sinA+sin120°cosA-cos120sinA)=2(sinA+√3/2cosA+1/2sinA)=2(3/2sinA+√3/2cosA)=2√3(√3/2 sinA+1/2 cosA)=2√3sin(A+60°)∵0