PrecalcAUnit3Project (4).pdf (complete)
.pdf
School
Michigan Virtual School**We aren't endorsed by this school
Course
ALL 2019
Subject
Mathematics
Date
Dec 19, 2024
Pages
2
Uploaded by CaptainTank9981
Precalculus A |Unit 3 Project: Angle of Elevation of the SunDirections: For this project, we are going to use what we know about right triangles to calculate the angle of elevation of the sun.Part 1To calculate the angle of elevation of the sun, use the following procedure: •Pick an easy to remember location (outdoors). Measure your height and the length of the shadow you cast at two different times of day (at least 3 hours apart) on two different days (e.g., 2pm and 6pm on Monday and Wednesday). Record the times at which you made your measurements and the measurements in a table (with units—inches or feet). 6 PointsDateTime AM/PMHeightShadow12/2/2411 am5’89 ft12/2/244 pm5’816 ft12/4/2411 am5’88 ft12/4/244 pm5’817 ft•Draw a sketch of the right triangle formed by you and your shadow for each scenario (based on your recorded data). Label the sides of your sketch with your measurements and angle of elevation. (The angle of elevation is currently unknown and can be called x). You should have four triangles total. 10 Points•Solve for the angle of elevation in each of your four triangleswhile clearly showing all of your steps. 10 Pointstan(x)=11/9 x = tan^-1(11/9) x=50.71tan(x)=4/16x= tan^-1 (4/16) x = 14.03tan (x) = 11/8 x = tan^-1(11/8) x = 53.97 tan (x) = 4/17 x = tan^-1 (4/17) x = 13.24
Part 2Once you have completed the calculations above, answer the following questions.•In several sentences, explain the right triangle drawings you used to model the shadow scenarios. Make sure to answer the following: 6 Points•What does each side length signify? What does the hypotenuse in your drawing signify in the real world?•Explain why the angle you chose on your triangle(s) is the angle of elevation of the sun. All of the triangles are supposed to be a representation of the elevation of the sun. As the triangles height is my height while the length of the triangle is supposed to be my shadow. And the last angle with line of sight. I chose this because it is the closest thing I could find to be equivalent to the elevation angle.•Using your measurements, when was your shadow the longest? What was the angle of elevation of the sun at this time? 2 PointsMy shadow was the longest on the fourth at 4 pm. The angle of elevation was 14•Using your measurements, when was your shadow the shortest? What was the angle of elevation of the sun at this time? 2 PointsMy shadow was the shortest on the second at 4 pm. The angle of elevation was 14•During what time of day do you think the shadow you cast will be longest? How do you know? 2 PointsI believe earlier in the day at 11 am it ill be the shortest. I know this because according to my calculations this is what is displayed.•During what time of day do you think the shadow you cast will be the shortest? How do you know? 2 PointsAlso, I believe that the shortest will be in the middle of the day at 4 pm. I know this because this is what I gathered from all fo my data and information.