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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 kmConsider A and B be two earth stations Let AB =4000 kmLet BC =y km and CD =x km, where CD is the height of the satellite from the earthFrom △ACDtan30∘=x4000+y⟹x4000+y=1√3⟹√3x=4000+y ........(1)From △BCDtan60∘=xy⟹xy=√3⟹y=x√3 ........(2)From (1) and (2)√3x=4000+x√3⟹3x=4000√3+x⟹2x=4000√3⟹x=2000√3km⟹x=2000×1.732=3464 km [∵√3=1.732]Hence, the distance of satellite from the earth is 3464 km

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