Answer:
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 = [tex]\frac{9}{2}[/tex] = 4.5 in.
Hypotenuse is a sides of rhombus.
Then, angle become [tex]\frac{108}{2}[/tex] = 54°. ( Diagonals of a rhombus bisect the angles).
By the cosine ration = [tex]\frac{adjacent}{hypotenuse}[/tex] .
cos( 54) = [tex]\frac{4.5}{hypotenuse}[/tex] .
0.58778 = [tex]\frac{4.5}{hypotenuse}[/tex] .
On dividing both sides by 0.58778.
Hypotenuse = [tex]\frac{4.5}{0.58778.}[/tex] .
Hypotenuse = 7.6559 inches
Approx = 8 inches
Therefore , Side of a rhombus = 8 inches.
