Triangle in a square

In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.

Correct result:

d =  2.1213 cm
e =  6.7082 cm
f =  6.7082 cm
E =  71.5651 °
F =  71.5651 °
D =  36.8699 °

Solution:

a=6 cm d2=(a/2)2+(a/2)2  d=a/8=6/8=2.1213 cm
e2=a2+(a/2)2=62+(6/2)2=45  e=1+1/4 a=1+1/4 6=3 5=6.7082 cm
f=e=6.7082=3 5=6.7082 cm
FEB=45  sinAED=a/e  AED=180πarcsin(a/e)=180πarcsin(6/6.7082)63.4349  E=180AEDFEB=18063.434945=71.5651=713354"
F=E=71.5651=71.5651=713354"
D=180FE=18071.565171.5651=36.8699=365212"



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