题目内容
如右图所示,在山脚A处测得该山峰仰角为θ,对着山峰在平坦地面上前进600 m后测得仰角为原来的2倍,继续在平坦地面上前进200 m后,测得山峰的仰角为原来的4倍,则该山峰的高度为( )
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A.200 m | B.300 m |
C.400 m | D.100 m |
B
分析:先根据题意可知AB=BP,BC=CP进而根据余弦定理可求得cos2θ的值进而求得θ,最后在直角三角形PCD中求得答案.
解:依题意可知AB=BP=600,BC=CP=200
∴cos2θ=
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∴2θ=30°,θ=15°
∴PD=PC?sin60°=200×
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故选B
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