A new building is being constructed a distance of 420 feet from the ocean, and the builder wants to have a rooftop patio with a view of the ocean. Another building, in between the new building and the ocean, is located a distance of 180 feet from the ocean and has a height of 15 feet. The angle of elevation from the ocean to the top of the new building, θ , represents the minimum angle for a person on the rooftop to view the edge of the ocean.
To the nearest hundredth, what is the measure of θ in degrees?
Construction for the new building has a maximum height restriction of 32 feet. Is it possible for the builder to have a rooftop patio with a view of the ocean? Justify your answer. In your response, make sure to define your variables and show all your work.
