The angle of depression of a point on the horizontal from the slope of a hill is 60°. If one has to walk 200m to reach the top from this point ,then the distance of this point from the base of the hill is
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The angle of depression of a point on the horizontal from the slope of a hill is 60°. If one has to walk 200m to reach the top from this point ,then the distance of this point from the base of the hill is
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Answer:
In △ABD,tan75=BDAD=OEAD __(1)
In △ACO,tan45=OCAO⇒1=OCAO⇒AO=OC
In △BCE,tan15=CEBE=CEOD __ (2)
From (1), AD = OE tan 75
(2), OD = CE tan 15
OA=AD+OD=OEtan75+CEtan15
In △CBE,cos15=BCCE⇒CE=BCcos15
⇒OA=OEtan75+BCtan15×cos15
⇒OA=(OC−CE)tan75+BCsin15
⇒OA=(OA−BCcos15)tan75+BCsin15
⇒OA(1−tan75)=BC(sin15−cos15.tan75)
⇒OA=1−sin75/cos75BC(sin15−cos15.sin75/