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Triangle DEF is equilateral. Find AE.

 

 

DA = 3, AF = 2

 Apr 11, 2024
 #1
avatar+14944 
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Find AE.

 

\(\triangle DEF\ is\ equilateral. \\ DA = 3,\ AF = 2,\ EF=5\\ \angle AFE=60°\)

Pythagorean trigonometric theorem: \(a²=b²+c²-2bc\cdot cos\ \alpha \)

 

\(\overline{AE}\ ^2=\overline{AF}\ ^2+\overline{EF}\ ^2-cos\ (AFE)\\\overline{AE}\ ^2=2^2+5^2-2\cdot 5\cdot cos\ 60^°\\ \overline{AE}= \sqrt{29-2\cdot 5\cdot0.5}\\ \color{blue }\overline{AE}= \sqrt{24}=4.899\)

 

laugh  !

 Apr 13, 2024

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