In this lab, you will be measuring the heights of your group members using the altitude angle of the sun and the length of the person's shadow. Each measurement will have to include the time at which it was taken since the sun's position in the sky changes throughout each day.
The mathematics behind calculating the height of the person in the above diagram is the use of the trig function tangent. In any right triangle the function tan q is equal to the ratio of (the length of the opposite side of the triangle) divided by (the length of the adjacent side of the triangle).
In our scenario, tan q = height/shadow.
So, our only question remains what is the angle of elevation of the sun? You can get that answer by consulting the website www.susdesign.com/sunangle/ and inputting your zip code and time of day that the shadow was measured. For example the data for Daytona Beach at 11:15 in the morning of July 21, 2012 was:
Now, you will go outside and measure the lengths of the shadows of your group members. Make sure that each person stands "up tall" so that his/her shadow is correctly representing their height. You will also need to record the time at which your take each measurement. When you return to the classroom you will also need to measure the actual height of each group member while standing up straight against a wall. To see how well both of your measurements agree, you will calculate a percent error for each member's height. The formula to do this is: |