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A parralelogram's two sides is 3 and 4.and an angle is 60.so,how i calculate its one digonal?(by using the formula of cos thita only)

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And hence you have a a right angles triangle,

We have

cosФ = AO/AD

and also Ф is 60/2 = 30 degress

cos (30)= AO/3

√3/2 = AO/3

AO= (3/2)√3

But the diagonal AC = two times A0

AC = 3√3.....

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Let the two sides be : AB and AD.

angle between the sides : AB and AD = Ф

the longer diagonal is : AC and let the shorter one BD.

AC² = AB² + AD² + 2 AB AD Cos Ф

= 3² + 4² + 2 * 3 * 4 * Cos 60°

= 37

AC = √37

the other diagonal is:

BD² = AB² + AD² - 2 AB AD Cos Ф

= 3² + 4² - 2 * 3 * 4 * Cos 60°

= 13

BD = √13

angle between the sides : AB and AD = Ф

the longer diagonal is : AC and let the shorter one BD.

AC² = AB² + AD² + 2 AB AD Cos Ф

= 3² + 4² + 2 * 3 * 4 * Cos 60°

= 37

AC = √37

the other diagonal is:

BD² = AB² + AD² - 2 AB AD Cos Ф

= 3² + 4² - 2 * 3 * 4 * Cos 60°

= 13

BD = √13