Answer:
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
