Exploring Angles Formed by a Pendant Chain
Pendant chains often create unique angles when worn. This investigation focuses on
understanding and analyzing the angle created by a pendant chain on the body.
In this investigation, the angle created by the chain of the pendant is explored and analyzed
using Geogebra and mathematical calculations. The aim of this IA is to determine the accuracy
of the angle measurement and investigate any percent error between Geogebra's calculation
and the one derived using the cosine rule.
Variables/all known values:
Geogebra values:
CB=2.4
BA=2.6
AC=2.7
Angle BAC=54.6°
Using the cosine rule to find the measure of angle BAC with calculations.
2
2
2
−1 2.6 +2.7 −2.4
𝑐𝑜𝑠 ( 2×2.6×2.7
) = 53. 81064°
Angle given by Geogebra = 54.6 degrees
Angle found using the cosine rule = 53.81064 degrees
Using the percent error formula
𝑒𝑥𝑎𝑐𝑡−𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 |
| 53.81064−54.6 | × 100 = 1. 444%
𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = ||
| × 100 = |
|
𝑒𝑥𝑎𝑐𝑡
54.6
The difference in percentage error between the angle (54.6 degrees) that Geogebra provides
and the angle (53.81064 degrees) that is determined by applying the cosine rule is roughly
1.444%. A 1.444% percentage inaccuracy can be seen as relatively insignificant in this context.
It suggests that there was a small difference in the two measurements. A percent error of less
than 5% is generally considered to be acceptable, indicating that there is not a statistically
significant discrepancy between the calculated number and the Geogebra measurement.
However, even a little percent inaccuracy could have an impact on the accuracy of results when
it comes to real-world applications or precision-based measures, such those in engineering
designs or scientific studies.
Supplementary Adjacent Angle found using sine rule and Original
Angle Measurement Differences, Including Comparative Percentage
Errors
In this continuation of the study, an examination of the supplementary adjacent angle that is
created when a horizontal straight line that crosses point A will be carried out. The goal is to find
the degree to which these additional angle match the original angle found in Geogebra. The
angle will be found using the sine rule.
In addition, a percentage inaccuracy between the calculated supplementary angle and the
corresponding angle from Geogebra will be obtained. This comparison study aims to determine
whether the difference in the percentage error of the initial angle matches the results when
looking at the additional angle. Analyzing the variation or consistency in percentage errors
between these angles would provide light on the accuracy and dependability of angle
measurements made using various techniques.
Finding the angle BAE using the Sine rule
First adjacent angle BAE
Angle given by Geogebra = 63.4 degrees
Angle found using the sine rule =
2.6
𝑠𝑖𝑛 58.9◦
=
2.7
𝑠𝑖𝑛𝑥◦
= 63.83397 degrees
Percentage error:
𝑒𝑥𝑎𝑐𝑡−𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 |
| 63.83397−63.4 | × 100 = 0. 6846%
𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = ||
| × 100 = |
|
𝑒𝑥𝑎𝑐𝑡
63.4
The newly calculated angle (63.83397 degrees) and the angle supplied by Geogebra (63.4
degrees) have a percent error of roughly 0.6846%. There is a noticeable disparity between this
percentage error and the 1.444% percentage error for the original angle measurement that was
previously acquired. The updated calculation displays a noticeably reduced % error, suggesting
that the two angle measurements are more in accord. This lower percentage error indicates that
the additional adjacent angle and the angle obtained from Geogebra are more closely aligned,
indicating that this measurement was more accurate than the initial angle evaluation. The
differing percentage errors between the two angle measurements show how different angle
calculations differ in terms of accuracy and dependability.
Criterion A: (Mark: 5) Justification: The investigation showcases exceptional coherence and
organization, presenting the supplementary angle analysis with impeccable structure and
seamless flow. The comprehensive layout greatly enhances readability and understanding,
setting a high standard for presentation.
Criterion B: (Mark: 3) Justification: While the report effectively utilizes mathematical language
and representation, there is slight room for enhancement in the depth of mathematical
principles' application and representation to attain a higher mark in this criterion.
Criterion C: (Mark: 2) Justification: The extension to explore supplementary angles
demonstrates solid personal engagement and a commendable independent inquiry, although
further depth or breadth in exploration could strengthen the overall engagement.
Criterion D: (Mark: 2) Justification: While there is reflection on the comparison between
percentage errors from the original angle and supplementary angles, additional depth or critical
insights into implications could enhance the reflection's quality.
Criterion E: (Mark: 5) Justification: The accurate calculation and interpretation of percentage
errors between the supplementary angles and Geogebra's measurements showcase precision
and alignment, displaying a high level of competency in mathematical calculations.
Total Marks: 17