Question

One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. Approximately how long is the side of the rhombus?

Answer 1

It will be 3.18.

Explanation:

A rhombus has degrees that add up to 360, and since opposite angles are congruent, to find the other opposites, subtract 360 by (102)*2, or 204. You get that each angle is 78 degrees. The triangle's other angle is 51 after you divide 102 by 2. That means sin78/4=sin51/x. Cross multiply and you get that x=3.18.

Answer 2

A rhombus is a quadrilateral which has 4 equal sides but two pairs of unequal angles. We are given one of the angles to be equal to 102 degrees so the other angle would have a measurement of 78 degrees. We calculate the length of the side as follows:
Triangle that is formed by two sides of rhombus and smaller diagonal is an isosceles triangle.

vertex angle = 78°
base angles = 51°
side opposite the vertex angle = 4
sides opposite the base angles = x

Using the law of sines,
x/sin(51) = 4/sin(78)
x = 4 * sin(51)/sin(78)
x = 3.18

Therefore, the length of the side would be 3.18.