在△ABC中a=sin10°,b=sin50°,C=70°,那么△ABC的面积为_.
问题描述:
在△ABC中a=sin10°,b=sin50°,C=70°,那么△ABC的面积为______.
答
S=
absinC=1 2
×sin10°sin50°sin70°1 2
=
cos10°sin10°cos40°cos20° 2cos10°
=
sin20°cos20°cos40° 4cos10°
=
=sin40°cos40° 8cos10°
sin80° 16cos10°
=
=cos10° 16cos10°
,1 16
故答案为:
.1 16