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.)

Side of a rhombus = 8 inches.

Step-by-step explanation:

Given : One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long.

To find :  Approximately how long is the side of the rhombus.

Solution : We have given that

Angle of a rhombus = 108° .

Shorter diagonal = 9 inches.

By the rhombus properties :

1) All sides of a rhombus are equal.

2) The diagonals of rhombus bisect each other at right angle.

Diagonal of the rhombus divide the rhombus in to four sides .

By the second property : The diagonals of rhombus bisect each other at right angle .

Adjacent side = = 4.5 in.

Hypotenuse is a sides of rhombus.

Then, angle become = 54°. ( Diagonals of a rhombus bisect the angles).

By the cosine ration = .

cos( 54) = .

0.58778 =   .

On dividing both sides by 0.58778.

Hypotenuse =   .

Hypotenuse = 7.6559 inches

Approx = 8 inches

Therefore , Side of a rhombus = 8 inches.