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______.

S=

1
2
absinC=
1
2
×sin10°sin50°sin70°
=
cos10°sin10°cos40°cos20°
2cos10°

=
sin20°cos20°cos40°
4cos10°

=
sin40°cos40°
8cos10°
=
sin80°
16cos10°

=
cos10°
16cos10°
=
1
16

故答案为:
1
16