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.) 7 in. 8 in. 11 in.

Answer 1

8 in.

Explanation:

Let's find the rhombus's length...

cosine =
`(adjacent)/(hypotenuse)`

cosine = ° = 54°

adjacent = = 4.5 in

Length of Rhombus = Hypotenuse

So...

cos54 =
`(9)/(x)`

x =
`(4.5)/(cos 54)`

x = 7.6558... about 8 inches

Answer 2

The value of the length of the rhombus will be found as follows:
cos θ=adjacent /hypotenuse
θ=108/2=54°
adjacent = 9/2=4.5 inch
hypotenuse=length of the rhombus
thus
cos 54=9/x
x=4.5/cos 54
x=7.6558~8 inches
the answer is 8 inches