Question

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.)

Answer 1

Hello,


cos (108°/2)=(9/2) / side
side =(9/2)/cos 54 °=7,655857275...(in)
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Answer 2

Side of a rhombus = 8 inches.

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 =
`(9)/(2)` = 4.5 in.

Hypotenuse is a sides of rhombus.

Then, angle become
`(108)/(2)` = 54°. ( Diagonals of a rhombus bisect the angles).

By the cosine ration =
`(adjacent)/(hypotenuse)` .

cos( 54) =
`(4.5)/(hypotenuse)` .

0.58778 =
`(4.5)/(hypotenuse)` .

On dividing both sides by 0.58778.

Hypotenuse =
`(4.5)/(0.58778.)` .

Hypotenuse = 7.6559 inches

Approx = 8 inches

Therefore , Side of a rhombus = 8 inches.