4. Find the tangent of each of the following angles: 5. Find the tangent of each of the following angles: 6. Find the arc tangent of each of the following numbers: 7. A vertical pole is 34 feet 8 inches high and stands in the center of a flat field. What angle does the sun's rays make with the earth's surface when the length of the shadow of the pole is 9 feet 1 inch? 8. Find the length of a line connecting the opposite corners of a rectangle having a width of 6.73 feet and a length of 16.95 feet. (Hint: Find the angle between the diagonal line and one side of the rectangle. Next, find the length of the diagonal line.) 9. A man wishes to know the distance from point C to point B across a lake. (See fig. F below.) (See fig. F below.) He measures the distance between points A and C and finds it to be 1,152 feet. He measures the angle between AC and AB and finds it to be 68°28'. He then measures the angle between BC and AC and finds it to be 90°. What is the distance between points C and B? FIGURE F C 10. A rope from the top of a 58.5 foot silo touches the ground at an angle of 41°17'. How far is it from the base of the silo to the point where the rope touches the ground? Approximately 2 or 3 weeks before you expect to take the endof-course test, you should request the test from the United States Armed Forces Institute, Madison 3, Wisconsin, or from the oversea USAFI with which you are enrolled. Obtain an application blank from your Education Officer, or from USAFI if necessary; fill it out carefully and make sure it has been properly certified by the USAFI Test Control Officer who will receive and administer the test. The test may be taken after you complete lesson 11 since lesson 12 is optional. 67 Lesson 10 The Reciprocal Scale On the front of the slide rule furnished by USAFI you will find the reciprocal or CI scale located in the center of the slide. As you can see, the CI scale has the same markings as the C scale. However, the CI scale is read from right to left, while the C scale is read from left to right. At first glance the CI scale may appear to be a rather useless addition to the slide rule. Although this scale will do nothing that cannot be done on the C and D scales, there are instances where it will save several movements of the slide. The primary advantage of the CI scale is the time saved in computing problems in multiplication and division. Considerable practice is necessary, however, to become fully acquainted with the accurate use of this scale. Text Assignment Chapter XII, pages 207-210, 213-217, 220-230. Omit "Basis of the Process," pages 211-213, and "Basis of the Process," pages 217-220. Study Notes Page 207. It is important that you read and understand the note at the bottom of this page in your text. multiplied by its reciprocal equals one? 1 1 Can you see that any number For example, the reciprocal and 9X=1. According to this, what is the reciprocal of of 9 is, and 9X=1. Page 208. Note that when multiplying with the CI and D scales the operation is similar to dividing with the C and D scales. To illustrate this consider the simple multiplication 8X6. Set the hairline of the runner over 8 on the D scale. Move the slide so that 6 on the CI also falls under the hairline of the runner. What number on the C scale appears under the hairline? It is 0.1667. In other words, 8×6 is the same as 8+1; or since 0.1667, it is the same as 8÷ 1 8 0.1667. The answer 48 is found on the D scale under the left index of the C scale. The above problem was used simply for demonstration purposes. Actually, there is no real value in using the CI scale to multiply one number by another. The real advantage is in the multiplication of three or more numbers as shown later in this lesson. Page 217. The answers to Practice Problems 10 and 14 are 3.02 and 2.57 instead of 3.03 and 2.58, respectively, as given in the text. Page 220. Earlier it was pointed out that a real advantage of the CI scale is in the multiplication of three or more numbers. Using just the C and D scales, the multiplication 17X23X4.07 requires the following steps: 1. Set the left index of the C scale to 17 on the D scale. 2. Move the hairline of the runner over 23 on the C scale. 3. Move the right index of the slide under the hairline. 4. Move the hairline of the runner over 4.07 on the C scale and read the answer under the hairline on the D scale. The answer is 1,591. If the same multiplication is performed using the C, CI, and D scales, the following steps are required: 1. Set the left index of the C scale to 17 on the D scale. 2. Move the hairline of the runner over 23 on the C scale. 3. Move the number 4.07 on the CI scale under the hairline of the runner and read the answer 1,591 on the D scale under the left index of the C scale. As you can see from a comparison of the two methods, the first two steps are identical. Most important, however, is the step saved in the second method. By saving steps you are usually able to increase your accuracy. Page 224. There is a definite advantage in using the CI scale along with the C and D scales when dividing a number by two or more numbers. The main difficulty is in determining the digit count. Also, there will be times when you will be unable to use the CI scale in such problems. This occurs when the second divisor on the CI scale falls beyond the D scale. In such cases use only the C and D scales to complete the problem. Page 229. The answer to Practice Problem 14 is 9.21 instead of 9.53 as given in your text. Also, a more precise answer for Practice Problem 17 is 0.320. Pages 229-230. Check your answers to the Review Problems with those given at the back of this study guide. Self-Examination Select the correct answer in each of the following exercises. |