A parallelogram has sides 20cm and 30cm with an angle of 80 between the two sides. What is the length of each of the diagonals?

length of diagonals are BD = 33.039 cm and AC = 38.84 cm

Step-by-step explanation:

given,

sides of parallelogram is 20 cm and 30 cm

Angle between them is 80°. opposite angle of parallelogram are same the opposite angle is same.

other angle = 360° - 80° - 80° + 2 x = 200

x = 100°

Using cosine law

c² = a² + b² - 2ab cos γ

In ΔDAB

BD² = 30² + 20 ² - 2 * 30 * 20 cos 80°

BD = 33.039 cm

now in ΔADC

c² = a² + b² - 2ab cos γ

AC² = 20² + 30² - 2 * 30 * 20 cos 100°

AC = 38.84 cm

length of diagonals are BD = 33.039 cm and AC = 38.84 cm