【答案】
分析:根据特殊角的三角函数值计算.
解答:解:锐角A满足2sin(A-15°)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/0.png)
,即sin(A-15°)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/1.png)
.
∵sin60°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/2.png)
,
∴A-15°=60°,
∴∠A=75°.
点评:本题考查特殊角三角函数值的计算,特殊角三角函数值计算在中考中经常出现,题型以选择题、填空题为主.
【相关链接】特殊角三角函数值:
sin30°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/3.png)
,cos30°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/4.png)
,tan30°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/5.png)
,cot30°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/6.png)
;
sin45°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/7.png)
,cos45°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/8.png)
,tan45°=1,cot45°=1;
sin60°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/9.png)
,cos60°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/10.png)
,tan60°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/11.png)
,cot60°=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131211105633965524290/SYS201312111056339655242001_DA/12.png)
.