A parallelogram has a 70 degree angle and sides 6 cm and 10 cm long. How long are its diagonals?

Let the shorter diagonal be x, then

x^2 = 6^2 + 10^2 - 2 x 6 x 10 x cos 70 = 36 + 100 - 120 cos 70 = 136 - 41.04 = 94.96

x = sqrt (94.96) = 9.7 cm

The other angle of the parallelogram is 1/2 (360 - 2 (70)) = 1/2 (360 - 140) = 1/2 (220) = 110

Let the longer diagonal be y, then

y^2 = 6^2 + 10^2 - 2 x 6 x 10 x cos 110 = 36 + 100 - 120 cos 110 = 136 + 41.04 = 177.04

y = sqrt (177.04) = 13.3 cm.

Therefore, the length of the diagonals are 9.7 cm and 13.3 cm.