In this assignment you will use your inclinometer to find the height of a building, a tree, and a telephone pole. Something similar can be done to find diameters of planets. You don’t have the equipment necessary to actually find the diameters of planets, but you can learn about the technique by determining heights of everyday objects on Earth.
You are going to find the angle between the horizon and the top of the building. Do it the same way you found the elevation of the Sun. Point the edge of the protractor at the top of the building, and read off the number of degrees between the string and the 90 degree mark on the protractor.
Let’s say the angle is 35 degrees. The height of the building equals the sine of 35, times the distance to the building, thus: height = tangent (35) x distance.
The tangent is an example of a trig function. Those of you who have taken algebra II are acquainted with trig functions (for better or worse). You don’t need to know what they are in order to do this project.
I will calculate the tangent of a range of angles for you:
tangent 10 = 0.176
tangent 15 = 0.268
tangent 20 = 0.364
tangent 25 = 0.466
tangent 30 = 0.577
tangent 35 = 0.700
tangent 40 = 0.839
tangent 45 = 1.0
45 degrees is the largest angle I want you to use. If your angle is bigger than 45, back up. Adjust your distance from the building until the angle from the horizon to the top of the building is one of the numbers in the list. 25 or 30, for example, rather than 28.
To calculate the height of the building, you also need the distance to the building. The most accurate method to get the distance is to use a tape measure. If not that, you could measure the length of your shoe, and walk heel to toe from your angle-measuring position, to the building, counting the little baby steps. Multiply the length of your shoe by the number of baby steps, to get the distance to the building. Worst of all, you can measure the length of a full stride, and count the steps to the building. The more accurate your distance to the building, the more accurate the calculated height.
The measured angle between the horizon and the top of the building is 35 degrees. The length of my shoe is 11 inches. After measuring the angle, I walked 90 baby steps to the building. 90 x 11 inches = 990 inches. 990 inches / 12 inches per foot = 82.5 feet.
h = tangent (35) x d
h = 0.700 x 82.5 feet
h = 57.8 feet
57.8 feet is actually how high the top of the building is above your eyeballs. How high is the top of the building above the ground? You figure it out.
Do this two more times, for a tree, and for a telephone pole.
Show all arithmetic operations, or NO CREDIT. Plus, I can’t give you feedback if I can’t see what you did.