Old Exam 4 Sol - Platt, David Oldquiz 4 Due: Dec 4 2005,...

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Unformatted text preview: Platt, David Oldquiz 4 Due: Dec 4 2005, 4:00 am Inst: Ken Shih 1 This print-out should have 28 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points The reflecting surfaces of two intersecting flat mirrors are at an angle of 69 , as shown in the figure. A light ray strikes the horizontal mirror at an angle of 45 with respect to the mirrors surface. 69 45 Figure is not drawn to scale. Calculate the angle . Correct answer: 42 . Explanation: Basic Concept: incident = reflected Solution: 1 2 Figure is to scale. The sum of the angles in a triangle is 180 . In the triangle on the left we have angles , 180 - 1 2 , and 180 - 2 2 , so 180 = + 180 - 1 2 + 180 - 2 2 , or 1 + 2 = 2 . (1) In the triangle on the right we have angles 1 , 2 , and . 180 = 1 + 2 + , so 1 + 2 = 180 - . (2) Combining Eq. 1 and 2, we have = 180 - 2 = 180 - 2(69 ) = 42 . As a matter of interest, in the upper-half of the figure the angles (clockwise) in the triangles from left to right are 45 , 45 , and 90 ; 90 , 21 , and 69 ; 111 , 24 , and 45 ; 135 , 24 , and 21 ; and in the lower-half of the figure the angles (counter-clockwise) in the triangles from left to right are 24 , 24 , and 132 ; 48 , 21 , and 111 ; 69 , 45 , and 66 ; 114 , 45 , and 21 . 002 (part 1 of 1) 10 points The reflecting surfaces of two intersecting flat mirrors are at an angle of 63 , as shown in the figure. A light ray strikes the horizon- tal mirror, reflects off the horizontal mirror, impinges on the raised mirror, reflects off the raised mirror, and proceeds in the right-hand direction. 63 Platt, David Oldquiz 4 Due: Dec 4 2005, 4:00 am Inst: Ken Shih 2 Figure is not drawn to scale. Calculate the angle . Correct answer: 54 . Explanation: Basic Concept: incident = reflected Solution: 1 2 Figure is to scale. The sum of the angles in a triangle is 180 . In the triangle on the left we have angles , 180 - 1 2 , and 180 - 2 2 , so 180 = + 180 - 1 2 + 180 - 2 2 , or 1 + 2 = 2 . (1) In the triangle on the right we have angles 1 , 2 , and . 180 = 1 + 2 + , so 1 + 2 = 180 - . (2) Combining Eq. 1 and 2, we have = 180 - 2 = 180 - 2(63 ) = 54 . As a matter of interest, in the upper-half of the figure the angles (clockwise) in the triangles from left to right are 46 , 46 , and 88 ; 92 , 27 , and 61 ; 119 , 17 , and 44 ; 136 , 17 , and 27 ; and in the lower-half of the figure the angles (counter-clockwise) in the triangles from left to right are 17 , 17 , and 146...
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Old Exam 4 Sol - Platt, David Oldquiz 4 Due: Dec 4 2005,...

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