The following data set shows the total number of people entering an exhibit per day: 163, 157, 166, 159, 160, 184, 162, 175, 177
, 164, 171, 170, 173, 176, 173, 178, 158, 163, 164, 169, 171, 160, 165, 182 Which intervals for the data values would be most appropriate for a frequency table?
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