Time - Angle - Shadow

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In early civilization, people have used the motion of the sun and the shadow an object creates as a measurement of time. In this experiment, we would better understand how these factors were used to tell the time back then. We would be indentifying the length of the shadow as well as the angle of elevation of the sun at four different times of the day. To get more accurate results, we would be using an object with a fixed height -in this case a bamboo stick 2.84m long.

Time: 9:30am

tan = oppositeadjacent
tan = 2.84 m2.34 m
tan = 1.2136 = tan-1(1.2136)
=    50° 30' 41.97"  

Time: 10:30am

tan = oppositeadjacent
tan = 2.84 m1.19m
tan = 2.3865
= tan-1(2.3865)
=    67° 15' 54.58"  

Time: 1:10pm
tan = oppositeadjacent tan = 2.84 m1.04.m
tan = 2.7307
= tan-1(2.7307)
=    69° 53' 12.99"  
Time: 2:15pm tan = oppositeadjacent tan = 2.84 m1.9m
tan = 1.4947
=    56° 12' 58.56"  
= tan-1(1.4947)

DATA TABLE
Time of the day| Shadow length(m) of an object with a fixed height of 2.84m| Angle of elevation of the sun| 9:30am| 2.32m| 50° 30' 41.97"|
10:30am| 1.19m| 67° 15' 54.58"|
1:10pm| 1.04m| 69° 53' 12.99"|
2:15pm| 1.9m| 56° 12' 58.56"|

Conclusion:
Sunlight shifts over the course of the day, hitting the earth directly around noon, from the east in the morning and from the west in the evening. At different times of the day, shadows get longer and shorter or may even disappear. People have relied on the sunlight’s changing directions and its effect on shadows as their basis to tell time.

The size of the shadow casted depends on...
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