From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?
For this case, what we must do is solve the following system of equations:  tan (50) = h / x  tan (40) = h / (x + 50)  Solving the system we have:  (x + 50) * tan (40) = h  (x) * tan (50) = h  Matching:  (x + 50) * tan (40) = (x) * tan (50)  Rewriting:  x (tan (50) - tan (40)) = 50 * tan (40)  x = 50 * tan (40) / (tan (50) - tan (40))  x = 118.9692621  Substituting:  h = (x) * tan (50)  h = (118.9692621) * tan (50)  h = 141.7820455  Answer:  The height of the building is:  h = 141.7820455 ft
