Lab 2

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Lab 2: Physics Related Trigonometry Clayton McCall 15 September 2023 PHY 211 – C01

OBJECTIVE: Create an experiment where you can use trigonometry in finding side lengths of a triangle made of a doorway. You will understand how trigonometry can help you in daily life The triangle above is a depiction of triangle 1 shown in the data below

The triangle above is a depiction of triangle 2 in the data below Triangle a b c Angle A Angle B Angle C 1 34" 81" 68" 25 19 137 2 48" 48" 68" 45 45 90 The data above shows the side lengths and angles that were found when looking and measuring each triangle

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Triangle A+B+C Accuracy % Error 1 181 56% 2 180 0 The data above that is shown is the % error of the angles that were found in the above triangles 1 and two. This percent error is found by adding all of the angles together subtracting 180 then multiplying that number by 100/180. Triangle a/sin(A) b/sin(B) c/sin(C) Average Range (min, max) 1 80.45 224.22 118.77 141.15 80.45,224.22 2 67.88 67.88 68 67.92 67.88,68 The data above shows the law of sines and how it is working in my triangles to get the data we are looking for we have to divide the side length by the sine of the corresponding angle. This data also shows the average of the sine laws and the range of the sine laws which is just the minimum and the maximum of each of the groups of sine laws. The data above shows the law of cosines and how it works in my two triangles to find the law of cosines in all triangles you have to follow a formaula which is (a^2+b^2-c^2)/2ab when you do this you find the law of cosines for that triangle. In triangle 1 I did (34^2+81^2-73^2)/2(34)(73) which got me .4810636583. once you have found the cos of your angle and the law of cosines for your triangle you can find the percent difference which is found by dividing the difference over the average then mulitpliing by 100 so I did -.73-.48 and got -1.21 then I found the average which was -.73+.48 which is -.25 divided by two is -.125 when you divide the two and multiply by 100 you can get 10.3 Triangle cos(C) % Differ- ence Error 1 -0.73 0.48 10.3% 2 0 -0.003 2

The data above is the law of tangents and how it works with my triangle as you can see since my right triangle has equal side lengths my % error is 0. To find the law of tangents you have to subtract the two sides then divide by the sum of the two which in my angle was 34-81/34+81 Which is 79.62. then to find the next part of the law of tangents you find the tangent of(25-19) over the tangent of(25+19) which is .13. then to find the % difference error you find the difference which is 79.62-.13 which equals 79.49 over the the average which is the sum over the amount of values which is 79.62+.13=79.75/2 which is 39.875 when you divide the two you get 39.875/79.49=.50163 multiplied by 100 is 50.2% How did you measure each of the quantities in Table 0? What was the error associated with each measurement? To measure each quantity I used a tape measure for length and my phone for the angles. The error with each measurement was most likely my phones angles being off or my holding of the tape measure incorrectly Was the error sufficiently small so that you believe you were able to verify these trigonometric relationships? In my right triangle the error was much smaller then the error of the other triangle so I was able to verify these relationships with a right triangle. Triangle % Differ- ence Error 1 79.62 0.13 50.2% 2 0 0 0

What kind of errors (systematic, random) did you encounter in doing this experiment? Was there one type of quantity that was harder to measure? If you used any of the cell phone applications, do you think they gave accurate results? The errors encountered were with the angles with my phone. It was very difficult to use the app and appropriate how I should even get the angle with my phone. I do not believe that the application that I used was accurate to what the angles actually were. Use the Law of cosines to calculate the final displacement for the man taking the following hike. The man first walks 10 kilometers in a direction 20 degrees East of North, then turns and walks 20 km in a direction 30 degrees West of north. How far is he from his starting point? Please use the Law of cosines and show your work To find the distance of how far the man is from his original spot first you have to find the angle c which can be found by turning the one triangle to two right triangles and subtracting angle a from 90 degrees then adding 30 degrees when you do that you find that angle c is 100 degrees once you’ve found angle c you can plug all of your information into the law of cosines which would be c^2=20^2+10^2-2(20)(10)cos(100) which would equal c=23.86 so the man in turn has traveled 23.86 kilometers from his original point. Cutnell and Johnson. Physics , 9 th ed. 2012

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