Intro: Using a Clinometer to Measure Height
In this Instructable, I'll show you how to use a clinometer to measure the height of a tall object (for help constructing your own clinometer from basic classroom materials, click here).
What you will need;
Pen or pencil
Step 1: Pick a Spot
Pick a spot to measure your object (I measured a telephone pole). You should be far enough away from your object that you can see the top of it, and you need to be on level ground with the base of the object. I like to set something down by my feet once I've picked my spot, so that I can easily come back to it.
Step 2: Measure Angle
Here's where we bust out our handy clinometer. Look through the straw of your clinometer at the top of the light pole (or whatever object you're measuring). The weighted string should hang down freely, crossing the protractor portion of the clinometer. Read the angle shown, and subtract from 90° to find your angle of vision from your eye to the top of the pole (it can be helpful here to have an assistant to read the measurement while you look through the straw). Record your results on your paper.
From my spot, my clinometer (read by my assistant) showed 55°. Subtracting from 90°, that indicated that I looked at an angle of 35° to the top of the telephone pole.
Step 3: Measure Distance
Once you have your angle of vision, use your tape measure to find the distance from the spot you're standing to the base of the object you're measuring (an assistant comes in handy here, too). We must know how far away you are to accurately calculate the height.
My spot was 15.6 meters from the base of the telephone pole I measured.
Step 4: Find Your Eye-height
The last piece of data you need to calculate the height of your object is the height from the ground to your eye (your eye-height). Have your assistant help you measure this using your tape measure.
My eye height was recorded for this example as 1.64 meters.
Step 5: Draw a Picture
Time to move inside. In calculating the height of the object you just measured, I find it helpful to begin by drawing a picture and labeling it with all of the information I have.
Step 6: Model As a Triangle
The next step is to simplify your drawing to model your system as a right triangle. Label your triangle with the angle you read on your clinometer as well as the distance you were standing from the object (we don't need the eye-height just yet).
Step 7: Solve for X
We can find x in this triangle (which represents the portion of the height from eye-level up) by using some basic trigonometry, specifically the tangent ratio of the triangle:
tan(angle) = x / distance
Multiply by the distance on both sides and you get:
x = tan(angle) * distance
Use a calculator to multiply these together and get a decimal value (be sure your calculator is in 'degrees' mode, rather than 'radians'!).
In my example:
tan(35°) = x / 15.6
x = tan(35°) * 15.6
x = 10.92 meters
Step 8: Combine With Eye Height
To find the height of your object, bring this x value back to the original drawing. By labeling it, we can see that the height of the object, h, is equal to the x value we just found plus the eye-height we measured earlier:
h = x + (eye-height)
In my example:
h = 10.92m + 1.64m
h = 12.56m
There you have it! A few basic classroom materials and a little bit of trigonometry and you can measure the height of anything around you!