Q15 of 61 Page 215

The angles of elevation of an artificial earth satellite is measured from two earth stations, situated on the same side of the satellite, are found to be 30° and 60°. The two earth stations and the satellite are in the same vertical plane. If the distance between the earth stations is 4000 km, find the distance between the satellite and earth. (√3 = 1.732)


Let C be position of station 1 and D of station 2 and BC = x.


Given, CD = 4000 km


Now, in triangle ABC,


∠ACB = 60°


We know,





⇒ AB = √3BC


⇒ AB = x√3 ……… (1)


And, in triangle ABD,


∠ADB = 30°


We know,






……… (2)


Now, equating (1) & (2), we get–



⇒ 3 x = x + 4000


⇒ 3x – x = 4000


⇒ 2x = 4000


⇒ x = 2000


And distance between the satellite and earth(AB) = x√3


= 2000(1.732)


= 3464 km


∴ Distance between the satellite and earth = 3464 km


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