在△ABC中,∠C=90°如果tanA= ,那么sinB的值是( ). A. B...
在△ABC中,∠C=90°如果tanA=,那么sinB的值是().A.B.C.D....
在△ABC中,∠C=90°如果tanA= ,那么sinB的值是( ). A. B. C. D.
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元元iS5
2014-12-08
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分析:先根据题意设出直角三角形的两直角边,根据勾股定理求出其斜边;再根据直角三角形中锐角三角函数的定义求解即可. ∵在△ABC中,∠C=90°,tanA= ![](https://iknow-pic.cdn.bcebos.com/bba1cd11728b47104e2b057ec0cec3fdfc032378?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) , ∴设BC=5x,则AC=12x, ∴AB=13x,sinB= ![](https://iknow-pic.cdn.bcebos.com/38dbb6fd5266d016041e669a942bd40735fa3578?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) = ![](https://iknow-pic.cdn.bcebos.com/e7cd7b899e510fb3191e8f25da33c895d1430c78?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . 故选B. 点评:本题考查锐角三角函数的定义及运用:在直角三角形中,锐角的正弦为对边比斜边,余弦为邻边比斜边,正切为对边比邻边. |
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