Diagonals

Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.

Result

u1 =  6.43
u2 =  7.66

Solution:

u12=a2+a2−2aacos⁡80∘ u12=2a2−2a2cos⁡80∘ u1=a2(1−cos⁡80∘)=6.43u_1^2 = a^2+a^2-2aa \cos 80 ^\circ \ \\ u_1^2 = 2a^2-2a^2 \cos 80 ^\circ \ \\ u_1 = a \sqrt{ 2(1-\cos 80 ^\circ )} = 6.43
 β=180∘−80∘=100∘ u22=a2+a2−2aacos⁡100∘ u22=2a2−2a2cos⁡100∘ u2=a2(1−cos⁡100∘)=7.66 \ \\ \beta = 180 ^\circ -80 ^\circ = 100 ^\circ \ \\ u_2^2 = a^2+a^2-2aa \cos 100 ^\circ \ \\ u_2^2 = 2a^2-2a^2 \cos 100 ^\circ \ \\ u_2 = a \sqrt{ 2(1-\cos 100 ^\circ )} = 7.66

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