Find measure of the longer disgonal

Question

A parallelogram has sides of length  units and  units. The shorter diagonal is  units. Find the measure of the longer diagonal. Round to 2 decimal places, if necessary.

Answer 1

Let T be one of the interior angles of the parallelogram that is opposite the shorter diagonal.

By the Law of cosines, 13^2 = 11^2 + 20^2 - 2(11)(20)cosT

cosT = 0.8

T = Arccos(0.8) = 36.8699 degrees

Each of the interior angles of the parallelogram opposite the longer diagonal is supplementary to T.

Let x be the longer diagonal. Then, by the Law of Cosines:

x^2 = 11^2 + 20^2 - 2(11)(20)cos143.13

x^2 = 872.9995

x = 29.55 units