Question

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.)

Answer 1

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 lon

Explanation:

Answer 2

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