Indirect measurement with a clinometer
It is not feasible to measure the height of a tall object by running a tape measure along its length and so we must measure it indirectly by measuring other quantities directly and using the proper mathematics to calculate the height.
We are going to make a clinometer and use it to measure angles of elevation from our line of sight to the top of a tall obect. Suppose we wanted to measure how tall a tree is, consider the following diagram:
1. The angle of elevation, e, is the quantity that we can measure with the clinometer. What other quantities can we measure directly? Label these on the diagram.
2. Using right triangle trigonometry, write down the trig ratio(s) that involve e.
3. Look at your answers to #1 and #2, which trig ratio involving which quantities will allow you to measure the height of the tree?
Since the angle of elevation plays an important role in your calculations you must measure it carefully. Let’s see what happens if we messed up the angle calculation by 5 or 10 degrees.
Now you are ready to find height with your clinometer. Pick out 2 objects from the list below that you wish to measure and go to it! Make sure to record your information carefully and take into account what we discussed about measuring the angle of elevation.
Find the height of…
(insert appropriate items for your school)
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