The Height of the School-Reflection
I employed a clinometer and a trundle wheel in the collection of data for this exercise. This is the observation method. I was directly in touch with the parameters for this exercise. I recorded the angles and their corresponding distances from the wall of the building as shown in the table below:
Angle (degrees) |
Trundle Wheel (meters) |
63 |
6.25 |
55 |
7.35 |
52 |
9.46 |
47 |
11.5 |
40 |
13.5 |
33 |
20.7 |
The data I obtained enabled me to calculate the actual height of the building. The formula employed for this exercise was that of the right triangle trigonometry. The figure below represents the pattern.
The table below shows how the height of the building was arrived at.
Angle (a) |
Distance (x) |
Height of the Building |
63 |
6.25 |
6.25 Tan 63 +1.54= 13.8 |
55 |
7.35 |
7.35 Tan 55 + 1.54= 12.0 |
52 |
9.46 |
9.46 Tan 52 + 1.54= 13.65 |
47 |
11.5 |
11.5 Tan 47 + 1.54= 13.87 |
40 |
13.5 |
13.5 Tan 40 + 1.54= 12.87 |
33 |
20.7 |
20.7 Tan 33 + 1.54 = 14.93 |
Where Tan a=h/x; h=x Tan a.
The height of the building is averagely 13.5 meters.
The estimated height of the building without calculation is between 12 and 16 meters with each level taking between 4 and 5 meters. The height of 13.5m that I obtained was therefore sensible.
There were several factors that determined the accuracy of this exercise. One would be the efficiency and accuracy level of the tools of measurement such as the clinometer and the trundle wheel. The second factor would be the sight of the person reading the angle and lastly, the height of the person recording the measurements. For example: If distance (x) was 11.5 m, angle (a) was 47 degrees and the height of the person recording the measurements was 1.54m, then the exact height of the building would be (11.5 tan 47 + 1.54) which is equal to 13.87m. If distance (x) was 11.4m, the height would be 13.76m. This gives a percentage error of 0.76% as shown: (13.87-13.76)/13.87*100=0.76%. This infers that for every 10cm away from the building, there is a likely error of 0.76% in the accuracy of the findings. This is a small margin that can be corrected. For an angle (a) of 46 degrees with a distance (x) of 11.5m, the height of the building would be 13.45m. This would result in a percentage error of 3.03 as shown: (13.87-13.45)/13.87*100=3.03%. This would be considered too high for a reasonable conclusion.
If the height of the person was altered to 1.5m, then the height of the building would be 13.83m with a percentage error of 0.29 as shown: (13.87-13.83)/13.87*100=0.29%. It was therefore necessary to have the correct angle as this posed a greater percentage error if used. The frequency of measurement also assists in having the right findings from the average of the figures obtained.
The advantage of trigonometry is that it can be used to accurately calculate heights of objects that we are not able to reach. We only need to know the angle of elevation of that object and the distance away from the base of that object. This method is used by engineers to find out the heights of buildings.