广西2020版高考数学一轮复习高考大题专项练二高考中的三角函数与解三角形文.docx

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1高考大题专项练二 高考中的三角函数与解三角形1.在平面四边形 ABCD中, ADC=90, A=45,AB=2,BD=5.(1)求 cos ADB;(2)若 DC=2 ,求 BC.2解 (1)在 ABD中,由正弦定理得 .BDsinA= ABsin ADB由题设知, ,5sin45= 2sin ADB所以 sin ADB= .25由题设知, ADB0, cosC= .5-12又 B+C= , sinB= .2 5-12

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