# A person in a hot air balloon sights two cities, one behind other. The angles of depression of the cities are 45 degrees and 30 degrees. If the hot air balloon is 750 m high, how far apart are the two cities?

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Let C₁ = distance from nearer city from the sight at 45 degrees

Height from the ground to air balloon = 750 m

tan 30⁰ =

C₂ =

C₂ =

tan 45 =

C₁ =

C₁ =

Distance (x)between two cities:

x = C₂ - C₁

x = 1,293 m - 750 m

Please click image below for my solution with illustration.