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+a22aacos80 u12=2a22a2cos80 u1=a2(1cos80)=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=18080=100 u22=a2+a22aacos100 u22=2a22a2cos100 u2=a2(1cos100)=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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