Trigonometry Lab Investigation
The Scenario
We have been tasked to measure the height of the climbing wall outside our school’s gym WITHOUT climbing up it. I joined with Merije and Ella to measure this length one sunny morning and our results weren’t perfect, but our we tried to make our attempt as accurate as possible.
Strategies
For this experiment we used trigonometry, SOHCAHTOA and Pythagoras’ Theorem to determine the height of the climbing wall.
Equipment
To gather the most accurate results we could we used a hand made inclinometer, which gives you the angle of elevation. We also used measuring tape to measure how far back from the wall we were, and of course a calculator to make our calculations accurate and quick (We also used pencils and paper to record out data!).
Results
We decided to stand 9 meters (900 cm) away from the base of the climbing wall. We used our inclinometer to measure the angle of elevation, which was 60 degrees (obtained by subtracting 90 degrees from the original measurement of 150 from the inclinometer). Therefore we were given both a side and an angle, giving us (as the triangle is a right angled triangle) the ability to use SOHCAHTOA/trigonometry.
From there I made the mistake of calculating the hypotenuse instead of the opposite side, giving me a measurement of 18 meters (1800 cm), but this would allow us to use pythagoras as well to measure the final side.
Using pythagoras’ theorem (a2+b2=c2) we were able to figure out the last measurement, which came to 15.6 meters.
Accuracy
After our calculations were complete we decided to go find the plaque near the climbing wall to find the real height, which turned out to be 7m. I am still not sure as to why our answer came to something so far from the answer, but I would assume it was something to do with the accuracy of our angle measurement. I did not personally measure the angle, thus have no idea as to the validity of the measurement taken, but when our group asked of the angle measured by the others in our class they all stated that they had found it to be around 20 degrees. A far fetch from our 60. But in terms of the strategies used they were all accurate.