Two tracking stations are on the equator 117 miles apart. A weather balloon is located on a bearing of Upper N 43 degrees Upper E from the western station and on a bearing of Upper N 15 degrees Upper E from the eastern station. How far is the balloon from the western​ station? Round to the nearest mile.

Accepted Solution

Answer:240.72 milesStep-by-step explanation:First, in the picture we have a drawing of this exercise. In this case, I will call A to the western station, and B the eastern station.According to this, we have a triangle there, and we need to calculate the distance between C and A (Distance AC). This is the diagonal of that triangle. We only have the length of side AB which is 117 miles, and now, to get the side AC we need to use the sin law.First, let's calculate the angle in B:<ABC = 15 + 90 = 105°This is the angle of that side of the triangle.The angle in A:<CAB = 90 - 43 = 47°The angle in C:<ACB = 180 - 47 - 105 = 28°We have the three angles now.Now the sin law is:Sin< = opossite leg / hypotenusehypotenuse = opposite leg / sin<Equaling both we have:hypotenuse = AB / sin<ACB = AC/sin<ABCAC = AB sin<ABC / sin<ACBSolving for AC we have:AC = 117sin105 / sin28AC = 240.72 miles