Q7 of 35 Page 219

As observed from the top of a hill 200 m high, the angles of depression of two vehicles situated on the same side of the hill are found to have measure 30 and 60 respectively. Find the distance between the two vehicles.

Let PQ be the hill with height = 200 m


R and S are two vehicles situated on the same side of the hill.


The angles of depression of vehicles R and S from P are 60⁰ and 30⁰ respectively, so


∠PRQ = ∠XPR = 60⁰


∠PSQ = ∠XPS = 30⁰


SR = Distance between the two vehicles



In ∆PQR,





In ∆PQS,




QS = 200√3


Distance between the two vehicles situated on the same side of the hill = SR


= QS – QR







= 230.6


The distance between two vehicles is 230.36 m.


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