One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long. Approximately how long is the side of the rhombus? (Hint: Diagonals of a rhombus bisect the angles.)

ANSWERS

2016-09-29 05:06:29

This is the concept of geometry, to get the length of the side of the rhombus we shall use the cosine rule; c^2=a^2+b^2-2abcosC c=9 C=(360-2*108)/2=[360-216]/2=72 Thus; since the sides of a rhombus are equal, then we can let the length of the sides be x; 9^2=x^2+x^2+2*x*xcos72 81=2x^2+0.62x^2 81=2.62x^2 hence; x^2=81/2.62 x^2=30.94 x=sqrt(30.94) x=5.56 The side lengths are each 5.56 inches long

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