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)

2
by wasimabiawas06

Answers

2015-05-03T19:44:11+05:30
We know that the diagonals are bisected at right angles in a parallelogram.

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.....
2015-05-03T20:45:28+05:30

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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

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