Calculating/ Find the Angle of Elevation of the Sun. Trigonometry is all around us! Right triangles can be found in many daily situations. In this project you will apply your knowledge of trigonometry to shadows in order to calculate the angle of elevation to the sun at different times of day.

To calculate the angle of elevation of the sun, use the following procedure: 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. Record the times and measurements (with units). Draw a sketch of the right triangle in this scenario. Label the sides of your sketch with your measurements and angle of elevation. Solve for the angle of elevation while clearly showing all of your steps.

To do the procedure above for two different times of day on two different days. After completed the calculations above, answer the following questions: All the components you will need to available in answer question 1-5 : - Tables of your height, shadow length (with units) and time of day. - Sketches of the four right triangles. - Label the sketches with your measurements and angle of elevation. - Use the correct trigonometric ratio.

- Show all steps and calculations when solving for the angle of elevation.

1. In several sentences, explain the right triangle drawings you used to model the shadow scenario. Make sure it answers the following: a) What does each side length signify? In particular, explain what does the hypotenuse in your drawing signify in the real world? b) Explain why the angle you chose is the angle of elevation of the sun. 2. From your measurements, when was your shadow the longest? What was the angle of elevation of the sun at this time? 3. From your measurements, when was your shadow the shortest? What was the angle of elevation of the sun at this time? 4. During what time of day do you think the shadow you cast will be longest? Use your knowledge of trigonometric ratios in your explanation. (Hint: Make sure you mention the angle of elevation, your height and a trig ratio that will help explain why the shadow is longest at this time of day).

5. During what time of day do you think the shadow you cast will be the shortest? Use your knowledge of trigonometric ratios in your explanation. (Use the hint from above, except this time you are explaining why the shadow is shortest at this time of day.)