A parallelogram has side lengths of 4 and 6 and an angle of measure 55°. Law of cosines: a2 = b2 + c2 - 2bccos (A) What is x, the length of the diagonal, to the nearest whole number? 3 5 6 7

There are two diagonals.

Law of cosines:

a^2 = b^2 + c^2 - 2bc cos (A)

One is:

x^2 = 4^2 + 6^2 - 2 (4) (6) cos (55°) = 46.75

=> x = √46.75 = 6.8 ≈ 7

Answer: 7

The other is:

x^2 = 4^2 + 6^2 - 2 (4) (6) cos (180° - 55°) = 79.53

=> x = √79.53 = 8.9 ≈ 9, which is not among the choices, so the answer is the 7.

Sorry, but I just took the pre-test and the answer is actually 5