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Question

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)

A
3446 km
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B
3464 km
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C
3488 km
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D
3400 km
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Solution

The correct option is B 3464 km
Consider A and B be two earth stations
Let AB =4000 km
Let BC =y km and CD =x km, where CD is the height of the satellite from the earth
From ACD
tan30=x4000+y
x4000+y=13
3x=4000+y ........(1)
From BCD
tan60=xy
xy=3
y=x3 ........(2)
From (1) and (2)
3x=4000+x3
3x=40003+x
2x=40003
x=20003km
x=2000×1.732=3464 km [3=1.732]
Hence, the distance of satellite from the earth is 3464 km

1899947_622377_ans_e5a13cf9ca4844f7ba4929a11eef36d4.jpg

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