Aparallelogram has a 7 inch side and a 9 inch side, and the longer diagonal is 14 inches long. find the length of the other diagona. do you need a calculator

the length of the other diagonal is ≈ 8

Step-by-step explanation:

Given that:

we can use the law of cosines to find out the angle that formed by the 7 inch side and 9 inch side (please have a look at the attached photo)

Let say ∠ABC, we have:

<=>

<=> cos(B) = -11/21

<=> ∠ABC = 121 degrees.

From the properties of parallelograms, we know that the sum of the 4 inter angles is 360 degrees.

2∠ABC + 2∠BAC =360

<=> ∠BAC = (360 - 2∠ABC) /2

<=> ∠BAC = (360 - 2*121) /2

<=> ∠BAC =59 degrees

Once again, we use can use the law of cosines to find out the length of the shorter diagonal

=  

= 65

<=> d = ≈ 8