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.
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.