Radio direction finders are set up at points A and B, 8.68 mi apart on an east-west line.?

From A it is found that the bearing of a signal from a transmitter is N 54.3 degrees E, while from B it is N 35.7 degrees W. Find the distance of the transmitter from B, to the nearest hundredth of a mile.

Please help, really confused!

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  • 9 years ago
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    ➊ Draw a diagram.

    • Point A and B are 8.68 mi apart on an E-W line.

    • Point "S" (for 's'ource of 's'ignal) is on a bearing N 54.3º E from point A, and

    • Point "S" is also on a bearing N 35.7º E from point B

    ➋ You should now be looking at an obtuse ∆ABS, with:

    • ∠A = 90 – 54.3 = 35.7º

    • ∠B = 90 + 35.7 = 125.7º

    • ∠S = 180 – 35.7 – 125.7 = 18.6º

    ➌ Apply the Law of SInes: a : sinA = b : sinB = s : sinS, where:

    • s = 8.68 miles

    • ∠A = 35.7º

    • ∠S = 18.6º

    and solve for side "a"

    (Can I leave that with you?)

    Hope this helps! Cheers! :)

    .

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  • 3 years ago

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