# Diagonals in diamond

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

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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#### Following knowledge from mathematics are needed to solve this word math problem:

Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator.

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