+30 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.
+129852 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
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
