[题目]一船在灯塔C的正东方向8海里的A处.以20海里/时的速度沿北偏西30°方向行驶．(1)多长时间后.船距灯塔最近?(2)多长时间后.船到灯塔的正北方向?此时船距灯塔有多远?(其中:162-82≈13．92) 题目和参考答案——青夏教育精英家教网—

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【题目】一船在灯塔C的正东方向8海里的A处，以20海里/时的速度沿北偏西30°方向行驶．

（1）多长时间后，船距灯塔最近?

（2）多长时间后，船到灯塔的正北方向?此时船距灯塔有多远?(其中:162-82≈13．92)

【答案】(1)12分钟后，船距灯塔最近；（2）此时船距灯塔有13.9海里.

【解析】试题分析：（1）作出图象在直角三角形ACD中求得AD的长后除以速度即可求得时间；

（2）在直角三角形ACB中求得AB的长后除以速度即可求得时间，由勾股定理可求出此时船距灯塔的距离．

试题解析：(1)如图所示，由题意可知，当船航行到D点时，距灯塔最近，

此时，CD⊥AB．

因为∠BAC=90°-30°=60°，所以∠ACD=30°．

所以AD==4(海里)．

又因为4÷20=0．2(小时)=12(分钟)，

所以12分钟后，船距灯塔最近．

(2)当船到达灯塔的正北方向的B点时， BC⊥AC．

此时∠B=30°，

所以AB=2AC=2×8=16(海里)．

所以16÷20=0．8(小时)=48(分钟)．

所以BC2=AB2-AC2=162-82≈13． 92．

所以BC≈13．9(海里)．

即48分钟后，船到灯塔的正北方向，此时船距灯塔有13.9海里．

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