What is the formula to find a parallelogram's diagonal?

Question

If anyone knows the answer please tell me!

Answer 1

Assuming you have the lengths of the sides and the angles, you can use the cosine rule to find the lengths of the diagonals (they are NOT equal).

a² = b² + c² - 2bc.cosA

b² = a² + c² - 2ac.cosB

c² = a² + b² - 2ab.cosC

Answer 2

You need the length of the sides and the angle opposite the diagonal.

Assume that the parallelogram has side lengths a and b and angles Φ and β, where Φ < β.

Use cosine law to find diagonals:

To find shorter diagonal, which will be across smaller angle Φ:

d² = a² + b² - 2ab.cosΦ

To find longer diagonal, which will be across larger angle β:

d² = a² + b² - 2ab.cosβ

Note, if you know only one of the angles, but need to find the other diagonal, remember that Φ + β = 180