Two tracking stations are on the equator 148 miles apart. A weather balloon is located on a bearing of N41°E from the western st
ation 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
1 answer:
Answer:
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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