【題目】一船在燈塔C的正東方向8海里的A處,以20海里/時的速度沿北偏西30°方向行駛.

1多長時間后,船距燈塔最近?

2多長時間后,船到燈塔的正北方向?此時船距燈塔有多遠?(其中:162-82≈1392)

【答案】(1)12分鐘后,船距燈塔最近;(2)此時船距燈塔有13.9海里.

【解析】試題分析:(1作出圖象在直角三角形ACD中求得AD的長后除以速度即可求得時間;

2)在直角三角形ACB中求得AB的長后除以速度即可求得時間,由勾股定理可求出此時船距燈塔的距離

試題解析:(1)如圖所示,由題意可知,當船航行到D點時,距燈塔最近,

此時,CDAB

因為∠BAC=90°-30°=60°,所以∠ACD=30°

所以AD==4(海里).

又因為4÷20=02(小時)=12(分鐘)

所以12分鐘后,船距燈塔最近.

(2)當船到達燈塔的正北方向的B點時, BCAC

此時∠B=30°,

所以AB=2AC=2×8=16(海里).

所以16÷20=08(小時)=48(分鐘)

所以BC2=AB2-AC2=162-82≈13 92

所以BC139(海里).

48分鐘后,船到燈塔的正北方向,此時船距燈塔有13.9海里.

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