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
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
its mainly because the pattern will be infinite and will never end. it will look like a gilder or like a filpbook when set to motion.