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In the diagram of rectangle ABCD, diagonal AC is drawn, DE = 8, DE is perpendicular to AC, and m∠DAC = 55.

To the nearest integer, the area of rectangle ABCD = how many square units.

TheBestAquamarine  May 1, 2017
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 #1
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In the diagram of rectangle ABCD, diagonal AC is drawn, DE = 8, DE is perpendicular to AC, and m∠DAC = 55.

To the nearest integer, the area of rectangle ABCD = how many square units.

 

sin (55)  =  DE / AD

AD  =  DE / sin (55)

AD  =  8 / sin (55)

And  

tan (55) = DC / AD

tan (55)  = DC / [8 / sin (55) ]

DC  =  8 tan (55) / sin (55)   

 

So...... the area of  ABCD  =

AD * DC  =

[8 /sin (55) ]  [ 8 tan (55) / sin (55) ]   ≈    136 units^2  

 

Here's a pic of 1/2 of the rectangle  

 

   

 

 

cool cool cool                

CPhill  May 2, 2017
 #2
avatar
0

In the diagram of rectangle ABCD, diagonal AC is drawn, DE = 8, DE is perpendicular to AC, and m∠DAC = 55.

To the nearest integer, the area of rectangle ABCD = how many square units.

 

sin (55)  =  DE / AD

AD  =  DE / sin (55)

AD  =  8 / sin (55)

And  

tan (55) = DC / AD

tan (55)  = DC / [8 / sin (55) ]

DC  =  8 tan (55) / sin (55)   

 

So...... the area of  ABCD  =

AD * DC  =

[8 /sin (55) ]  [ 8 tan (55) / sin (55) ]   ≈    136 units^2  

Guest May 2, 2017

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