Every time I write an exam, I think about this story, where a physics professor asks on an exam how to measure the height of a building using a barometer. A student answered that he would tie a string to the barometer, lower it down, then measure the length of the string. Given no credit, he protests, and the professor offers him a second chance to provide an answer that is both correct and demonstrates some knowledge of physics taught in the course. The student goes on to give several answers (in some versions the student is averred to be Niels Bohr - though the origin of the story is apparently in a textbook on the teaching of math and science by Alexander Calandra, and unrelated to Bohr) all demonstrating a knowledge of physics, and none the one he seems to know the professor is fishing for (which has to do with the - probably unmeasurably small - pressure differential between the ground and the top of the building).
Here is a chemistry exam question I sometimes ask - how would you measure the height of a mountain with a thermometer? This is a well-known technique,not a trick question, the apparatus is called a hypsometer, from the Greek for "height-measure". The underlying science is that the boiling point of a liquid changes in a known way with altitude. Hypsometers were used before portable aneroid barometers became widely available, and were used in high altitude balloon measurements of pressure as late as the 1960s.
Bonus question: Is it easier to drink a liquid using a straw at the top of Mt. Everest or on the beach in Florida? (Disregard temperature differences and explain your answer for full credit!)