Two tracking stations are on the equator 148 miles apart. a weather balloon is located on a bearing of n41°e from the western station and on bearing of n21°e from the eastern station. how far is the balloon from the western station? round to the nearest mile from the nearest station. a 404 mil b 382 mi c 413 mil d 373 mi

  A  404 mi

Step-by-step explanation:

If we designate the points of the triangle A, B, and C for the locations of the western station, eastern station, and balloon, respectively, we have the following:

  ∠CAB = 90° - 41° = 49°

  ∠CBA = 90° + 21° = 111°

  ∠ACB = 41° -21° = 20°

side "c" (opposite ∠ACB) is 148 miles

The distance we're asked to find is AC = b, the longest side of the triangle. The law of sines tells us ...

  b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = (148 mi)·sin(111°)/sin(20°) ≈ 403.98 mi ≈ 404 mi

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step-by-step explanation:

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