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!
- Neil KelceyLv 69 years agoFavorite Answer
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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