题目内容
如图,一量角器所在圆的直径为10cm,其外缘有A、B两点,其读数分别为71°和47°.(1)劣孤
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_ST/0.png)
(2)求劣孤
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_ST/1.png)
(3)问A、B之间的距离是多少?(sin12°≈0.20,cos12°≈0.98)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_ST/images2.png)
【答案】分析:(1)劣孤
所对的圆心角的度数就是度数71度与47度的差;
(2)根据弧长的计算公式即可求解;
(3)经过圆心O作弦AB的垂线,在直角三角形中利用三角函数即可求解.
解答:
解:(1)71°-47°=24°
(2)
=
×
×π=
π
(3)过O作OC⊥AB于点C.
∵∠AOB=24°
∴∠AOC=12°
∴AC=OA•sin12°=5×0.20=1cm.
∴AB=2AC=2cm.
点评:本题主要考查了弧长的计算公式,圆中求弦长,半径,弦心距的计算一般可以转化为解直角三角形.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/0.png)
(2)根据弧长的计算公式即可求解;
(3)经过圆心O作弦AB的垂线,在直角三角形中利用三角函数即可求解.
解答:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/images1.png)
(2)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022155127915803586/SYS201310221551279158035020_DA/4.png)
(3)过O作OC⊥AB于点C.
∵∠AOB=24°
∴∠AOC=12°
∴AC=OA•sin12°=5×0.20=1cm.
∴AB=2AC=2cm.
点评:本题主要考查了弧长的计算公式,圆中求弦长,半径,弦心距的计算一般可以转化为解直角三角形.
![](http://thumb2018.1010pic.com/images/loading.gif)
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