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
