Using trigonometry to measure a flagpole!
September 24, 2019
The Challenge
The task at hand was to calculate the height of a flagpole using only two angles and one measurement.
Flag Pole Lab
The Angle
My partner and I started by picking a spot a few meters away from the base of the flagpole. We chose one that had markings; this way, we could find it later. Using a clinometer and a steady hand, we carefully noted the angle from the very top of the pole. This was about 62 degrees.
The Lengths
The next step was to measure the height of my partner’s eyes from the ground. Unfortunately, we ended up using a tape measure that was in imperial units. We wrote the numbers down to convert later.
Then, we measured the length between the middle of the pole and my partner. We estimated where their eyes would be and started the measure there. After recording that number, we were ready to head back and start doing some calculations.
The Calculations
To begin, my partner and I converted our measurements to metric, leaving a few decimal placements for at least some accuracy.
To figure out the height of the flagpole, we used the tan ratio. Our unknown variable gets divided by the length that we already know, Rearranged, this means we must multiply tan(62) by the length. This, however, will only give us the height of the top of the pole, not including everything below eye level. Before stating the final result, we must add the height of eye level to the rest.
The Reflection
Having our final result, we noticed that it varied quite a bit with what the other groups got. While it’s a bit more than a reasonable margin of error, we think the combination of measuring in imperial units and measurement inaccuracies. After double-checking the math a few times, we agreed that the instruments we used only give us rough measurements.
