In the center of a growing city is an old church and a high-rise office building separated by a plaza. Two surveyors are collaborating on the job of determining how high the tip of the church spire is above the plaza. Each surveyor has a theodolite mounted on a tripod. One surveyor is in the entrance way of the high-rise. The top of his tripod is 165cm above plaza level. The second surveyor is directly above the first, and (amazingly) the top of her tripod is exactly 100m above the top of her colleague's tripod. The first surveyor measures the angle of elevation of the tip of the spire as 50∘. The second surveyor measures the angle of depression of the tip of the spire as 30∘. (The diagram on the right is not drawn to scale. Points A and F are at plaza level. You'll have to supply all the necessary measurements on the diagram for yourself.) Correct to 2 decimal places, how high is the tip of the spire above the plaza?
m