# One of the sides of a parallelogram is 8. One of the angles is 70. Find the length of the diagonal. Use Cosine or whatever works.

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### 1 Answer

There is not enough information to solve this problem.

(a) Assume the parallelogram is a rhombus; i.e. all sides are 8.

Then the length of the shorter diagonal d can be found using the Law of Cosines: `d^2=8^2+8^2-2(8)(8)cos70^@` so `d^2~~84.221` and `d~~9.18` .

Since the consecutive angles of a parallelogram are supplementary another angle is 110. So we can find the length of the longer diagonal D by `D^2=8^2+8^2-2(8)(8)cos110^@` so `D^2~~171.779` and `D~~13.11`

(b) Assume that 8 is the length and 6 the width of the parallelogram:

`d^2=8^2+6^2-2(8)(6)cos70^@` and `d^2~~67.166==>d~~8.20` and

`D^2=8^2+6^2-2(8)(6)cos110^@` and `D^2=132.834 ==> D~~11.53`

(c) If 8 is the length and x is the width then:

`d^2=x^2+8^2-16xcos70^@` . Without some way of determining the width, you cannot get an "answer", just an expression that involves the width as a variable.