how high is the satellite?

Question

The figure below shows a satellite orbiting Earth. The satellite passes directly over two tracking stations 𝐴 and 𝐵, which are 71 miles apart. When the satellite is on one side of the two stations, the angles of elevation at 𝐴 and 𝐵 are measured to be 83.9∘ and 86.2∘ respectively. How far is the satellite from station 𝐴

and how high is the satellite above the ground? Round answers to the nearest whole mile.

Answer 1

By Sine Law: 71/sin2.3° = x/sin(180° - 86.2°); x = 71sin93.8°/sin2.3° = 181.31 mi = 181 mi

h = xsin83.9° = 181.31·sin83.9ˆ = 180 mi