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Unformatted text preview: MIDTERM 4 SOLUTIONS (CHAPTERS 5 AND 6) MATH 141 SPRING 2011 KUNIYUKI 150 POINTS TOTAL: 57 FOR PART 1, AND 93 FOR PART 2 Show all work, simplify as appropriate, and use good form and procedure (as in class). Box in your final answers! No notes or books allowed. Write units in your final answers where appropriate. Try to avoid rounding intermediate results; if you do round off, do it to at least five significant digits. We assume that all vectors on this test are in the usual xyplane. PART 1: SCIENTIFIC CALCULATORS ALLOWED! (57 POINTS TOTAL) 1) Find the length of Side c for the triangle below using the Law of Sines. Round off your answer to the nearest tenth (i.e., to one decimal place) of an inch. (9 points) Find Angle B . B = 180 80 44 = 56 . Use the Law of Sines. We now know B , b , and C , and we want to find c . b sin B = c sin C 41 sin56 = c sin44 c = 41sin44 sin56 c 34.4 inches This makes sense, because c is shorter than b , and Angle C is smaller than Angle B . Remember that smaller angles face (eat) shorter sides in a triangle. 2) A slanted lightning rod, represented by line segment BC in the figure below, has length 17.1 feet. An observer stands at point A . The observers shoes are 12.7 feet from the base of the rod and are 23.4 feet from the top of the rod. Find the measure of Angle A , the angle of elevation from the observers shoes to the top of the rod, using the Law of Cosines. Round off your answer to the nearest tenth of a degree. Note: Angle C is obtuse, not right. (10 points) Use the Law of Cosines. a 2 = b 2 + c 2 2 bc cos A cos A = b 2 + c 2 a 2 2 bc cos A = 12.7 ( ) 2 + 23.4 ( ) 2 17.1 ( ) 2 2 12.7 ( ) 23.4 ( ) = 416.44 594.36 0.70065 A = cos 1 416.44 594.36 (in degrees) A 45.5 (Make sure you are in degree mode when you press the cos 1 button. You dont have to worry about Quadrant issues here, due to the range of the inverse cosine function..) Note: B 32.0 and C 102.5 . 3) Consider the vectors v and w , where v = 7, 2 and w = 3,12 . (9 points total) a) Find the vector v w ( ) w . Write your answer in x , y component form. (5 points) Observe that v w is a scalar, and v w ( ) w , which is a scalar times a vector, is a vector. v w = 7, 2 3,12 = 7 ( ) 3 ( ) + 2 ( ) 12 ( ) = 21 + 24 = 3 Therefore, v w ( ) w = 3 w = 3 3,12 = 3 3 ( ) , 3 12 ( ) = 9, 36 b) Does v w ( ) w have the same direction as the vector w ? (2 points) Y e s N o Since w is a nonzero vector, then any positive scalar times w is a vector that has the same direction. the same direction....
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This note was uploaded on 09/08/2011 for the course MATH 141 taught by Professor Staff during the Fall '11 term at Mesa CC.
 Fall '11
 staff
 Math, Calculus

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