Question

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.)

Answer 1

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)