Throughout this lab we will use the \"smallangle\" formula. This is an easy formula that describes the relationship between size. angular size. and distance. Here we will use a variant of the formula which specically uses degrees: size angular size = x 57.3 degrees. distance The exact formula involves simple trigonometry. but because we will be measuring small angles. we will manage just ne with this approximate formula. Each time we use this formula the meanings of size. angular size. and distance will change. but the basic underlying principle will be the same. I. Building an Angletron Before we can measure the angular size of the Moon. we need to build a tool to help us measure small angles. Protractors are ne for measuring large angles. but we need something better for measuring small angles. Let's call our tool for measuring small angles an \"Angletron.\" Here's how to build one: o lCut out a strip of paper or cardboard about 3 inches wide and 8.5 inches long. 0 Hold the paper at arm's length in front of you and measure the distance from the paper to your eyes. You can measure the distance directly with a tape measure. or you can measure the distance with a string rst and then measure the length of the string with a ruler. Get a friend to help you measure the distance. if possible. If you wish. you can repeat the measurement and take an average. to achieve higher accuracy. Record the technique you used to measure the distance. and the answer you obtained. 0 Now we want to make marks on the paper that will be 1 degree apart. when the paper is held at arm's length. We use the smallangle formula to calculate how far apart these marks should be. 1We have already measured the distance we need to use in the formula. We want the angular separation (i.e.. the angular size) of the marks to be 1 degree. The formula tells us how far apart our two marks need to be. (The distance between the marks will be given by the \"size\" in the formula.) Show your calculation of the spacing between tick marks. 0 Now use a ruler to place big tick marks on the piece of paper we cut out above. The marks should be separated by the amount we calculated with the smallangle formula. Label the big tick marks 0 degrees. 1 degree. 2 degrees. etc. 0 Divide the space between each big tick mark into 4 equally sized intervals by drawing 3 smaller tick marks between the major tick marks. These smaller tick marks will be 1/4 of a degree apart when the paper is held at arm's length. \"Then you are done using your Angletron. take a photograph of it and submit it with your lab writeup. II. Measuring the Moon Now that we have constructed an Angletron. we can use it to measure the diameter of the Moon. For best results. the Moon's phase should not be a thin crescent (since it's more diicult to discern the full diameter). 0 Hold your Angletron at arm's length. so that it partially covers the Moon. Note how many small tick marks it takes to cross the diameter of the Moon and how many degrees this corresponds to. Estimate fractions of a small tick spacing in your measurements (i.e.. you might get a measurement of 2.3 small tick marks). Record your