Two airplanes at points A and B as shown in the diagram belo

Two airplanes at points A and B as shown in the diagram below have elevations of 23,000 feet and 18,000 feet respectively. Both are flying east toward an airport control tower at T. From T, the angle of elevation of the airplane at A is 4 degree, and the angle of elevation of the airplane at B is 2.5 degree. How far apart (in miles) are the airplanes?

Solution

<ATB=4-2.5=1.5degree

using cosine law

x²=23000²+18000²-2(23000)(18000)cos 1.5

x²=853000000-828000000cos1.5

x=5028.29miles