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 answer:

d =  2.1213 cm
e =  6.7082 cm
f =  6.7082 cm
E =  71.5651 °
F =  71.5651 °
D =  36.8698 °

Step-by-step explanation:

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   sin  AED  = a/e  AED=π180°arcsin(a/e)=π180°arcsin(6/6.7082)63.4349  E=180AEDFEB=18063.434945=71.5651=71°3354"

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
The Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: