In this exercise you are going to use the law of cosines
Chapter 9, Problem 58(choose chapter or problem)
In this exercise you are going to use the law of cosines and the law of sines to determine the area of the shaded equilateral triangle in Figure A. Begin by labeling points, as shown in Figure B.(a) Apply the law of cosines in ^ABE to show thatAE (b) Apply the law of sines in ^ABE to show thatsin( ) (3 )/(2 ).(c) Apply the law of sines in ^CFB to show thatsin( ) ( )/(2 ). Hint: ^AEB iscongruent to ^BFC, so BF AE.(d) Apply the law of sines in ^QEB to show thatQE (e) Apply the law of sines in ^QEB to show thatQB (f) Show that PQ 3 /7.Hint: PQ AE (QE AP), and by symmetry,AP QB.(g) Use the result in part (f) to find the area of equilateraltriangle PQR.
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