Parallelogram 82695

Given is the parallelogram KLMN, in which we know the side sizes/KL/ = a = 84.5 cm, /KN/ = 47.8 cm, and the angle size at the vertex K 56°40'. Calculate the size of the diagonals.

Correct answer:

u1 =  117.7461 cm
u2 =  70.6119 cm

Step-by-step explanation:

a=84.5 cm b=47.8 cm K=56°40=56°+6040°=56.6667°56.6667  sin K = h:b  h=b sinK=b sin56.666666666667° =47.8 sin56.666666666667° =47.8 0.835488=39.93632 cm  x=b cosK=b cos56.666666666667° =47.8 cos56.666666666667° =47.8 0.549509=26.26653 cm  u1=h2+(a+x)2=39.93632+(84.5+26.2665)2=117.7461 cm
L=180K=18056.6667=3370123.3333   sin L = g:a  g=a sinL=a sin123.33333333333° =84.5 sin123.33333333333° =84.5 0.835488=70.59872 cm  y=a cosL=a cos123.33333333333° =84.5 cos123.33333333333° =84.5 (0.549509)=46.43351 cm  u2=g2+(b+y)2=70.59872+(47.8+(46.4335))2=70.6119 cm



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