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ABCD is a square with E, F, and G being the midpoints of CD, BC, and EF respectively. Let ∠DGE=x. Find tanx.

 

 Jun 30, 2020
 #1
avatar+1421 
0

Let DC be 1 unit

 

Angle       x = [arctan ( 0.75 / 0.25 )] - 45º  smiley

 Jun 30, 2020
 #2
avatar+25597 
+2

ABCD is a square with E, F, and G being the midpoints of CD, BC, and EF respectively. Let \(\angle\)DGE=x.

Find \(\tan(x)\).

 

\(\begin{array}{|rcll|} \hline \tan(y) &=& \dfrac{1}{4}\above 1pt \dfrac{3}{4} \\\\ \tan(y) &=& \dfrac{1}{4} * \dfrac{4}{3} \\\\ \tan(y) &=& \dfrac{1}{3} \\ \mathbf{y} &=& \mathbf{\arctan\left(\dfrac{1}{3}\right)} \\ \hline x+y &=& 45^\circ \\\\ x &=& 45^\circ - \arctan\left(\dfrac{1}{3}\right) \\ x &=& 45^\circ - 18.4349488229^\circ \\ \mathbf{x} &=& \mathbf{26.5650511771^\circ} \\ \hline \end{array}\)

 

laugh

 Jun 30, 2020

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