Question

求教大神！这道题怎么解的啊？

Answer 1

连接右圆直径、半径，则∠1和∠2为同一圆弧所对圆周角和圆心角，

∴ ∠2=2∠1,

小长方形对角线=√(10²+5²)=5√5

 tan∠1=5/10=1/2，

 sin∠1=5/(5√5)=1/√5，

 cos∠1=10/(5√5)=2/√5

∠1=26.565°

∠2=53.13°

∠3=180°-53.13°=126.87°

S弓形= πx5x5x（126.87/360）- 5xsin∠1x5xcos∠1÷2x2

=3.14x5x5x(126.87/360)- 5x 1/√5x5x2/√5÷2x2=27.665-10=17.665cm²

s面积= 5x10÷2-17.665-(10x20-3.14x5x5x2)÷8

=25-17.665-5.375=1.96 cm²

所以，阴影面积=20x10÷2-3.14x5x5-1.96=100-78.5-1.96=19.54cm²