Hi! ! 10 pts. one angle of a rhombus is 120° and the length of its shorter diagonal is 9. what is the perimeter of the rhombus? draw a diagram and show your work. : )

This is the concept of geometry, we are required to calculate for the length of the sides of the rhombus; we know that a rhombus is a compressed square, this implies that all the sides are equal;

If one of the angles is 110° the other angle will be:

180-110=70°

thus using the cosine rule we can find the side lengths as follows;

c^2=a^2+b^2-2ac Cos C

thus

let side a=b=x in

shorter diagonal=c=4 in

C=70°

substituting this into the formula we get:

4^2=x^2+x^2-2*x*x Cos 70

4^2=2x^2-2x^2(0.3420)

16=2x^2-2x^2(0.3420)

dividing through by 2 we get;

8=x^2-0.3420x^2

8=0.6580x^2

x^2=12.15843

getting the square root of both sides get:

x=sqrt(12.15843

x=3.4869) 

x=3.5 (1 d.p)

the length of the sides is 3.5

step-by-step explanation: