A parallelogram has sides of lengths 8 and 6, and one angle is 55°. find the lengths of the diagonals. (round your answers to two decimal places. enter your answers as a comma-separated list.)

Here shall use the cosine rule:

let the length of the first diagonal be d;

thus

d²=8²+6²-2*6*8cos55

d²=64+36-96cos55

d²=44.93666211

d=6.7035

We know that two adjacent angles of parallelogram are supplementary, so since 180-55=125°, the length of the second diagonal d', we shall have:

d'²=8²+6²-2*8*6cos 125

d'²=64+36-96cos125

d'²=155.0633379

d=12.45244

Answers: (6.7035,12.45244)