# Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.

Correct result:

u1 =  160
u2 =  277.13

#### Solution:

$u_1^2 = a^2+a^2-2aa \cos 60 ^\circ \ \\ u_1^2 = 2a^2-2a^2 \cos 60 ^\circ \ \\ u_1 = a \sqrt{ 2(1-\cos 60 ^\circ )} = 160$
$\ \\ \beta = 180 ^\circ -60 ^\circ = 120 ^\circ \ \\ u_2^2 = a^2+a^2-2aa \cos 120 ^\circ \ \\ u_2^2 = 2a^2-2a^2 \cos 120 ^\circ \ \\ u_2 = a \sqrt{ 2(1-\cos 120 ^\circ )} = 277.13$

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