SOLUTION: The vertices of parallelogram ABCD are A(0,0), B(7,0), (12,8), and D(5,8). Find, to the nearest degree the measure of angle DAB. I don't get this at all! All I know is that the

Algebra ->  Algebra  -> Angles -> SOLUTION: The vertices of parallelogram ABCD are A(0,0), B(7,0), (12,8), and D(5,8). Find, to the nearest degree the measure of angle DAB. I don't get this at all! All I know is that the      Log On

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Question 143302: The vertices of parallelogram ABCD are A(0,0), B(7,0), (12,8), and D(5,8). Find, to the nearest degree the measure of angle DAB.
I don't get this at all! All I know is that the measure of side AB is 7 and the measure of side CD is also 7.
Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
The vertices of parallelogram ABCD are
A(0,0), B(7,0), (12,8), and D(5,8). Find,
to the nearest degree the measure of angle DAB.
I don't get this at all! All I know is that the
measure of side AB is 7 and the measure of side CD is also 7.

drawing%28300%2C300%2C-2%2C13%2C-2%2C13%2C+line%280%2C0%2C7%2C0%29%2Cline%287%2C0%2C12%2C8%29%2Cline%285%2C8%2C12%2C8%29%2C%0D%0Aline%280%2C0%2C5%2C8%29%2Cgraph%28300%2C300%2C-2%2C13%2C-2%2C13%29%2C%0D%0Alocate%28.5%2C1%2CA%29%2C+locate%286.5%2C1%2CB%29%2C+locate%2812%2C9%2CC%29%2C+locate%285%2C9%2CD%29%0D%0A%0D%0A+%29 

First draw a perpendicular DE to AB

drawing%28300%2C300%2C-2%2C13%2C-2%2C13%2C+line%280%2C0%2C7%2C0%29%2Cline%287%2C0%2C12%2C8%29%2Cline%285%2C8%2C12%2C8%29%2C%0D%0Aline%280%2C0%2C5%2C8%29%2Cgraph%28300%2C300%2C-2%2C13%2C-2%2C13%29%2C%0D%0Alocate%28.5%2C1%2CA%29%2C+locate%286.5%2C1%2CB%29%2C+locate%2812%2C9%2CC%29%2C+locate%285%2C9%2CD%29%2C%0D%0Aline%285%2C8%2C5%2C0%29%2C+locate%284.3%2C1%2CE%29%0D%0A%0D%0A+%29 

Because D's coordinates are (5,8), we know that AE=5, DE=8

ADE is a right triangle.

DE is the side opposite angle DAB and
AE is the side adjacent angle DAB,

and since TANGENT+=+%28OPPOSITE%29%2F%28ADJACENT%29

tan%28DAB%29+=+%28DE%29%2F%28AE%29+=+8%2F5+=+1.6

Now, with calculator in DEGREE mode, use the TAN%5E%28-1%29
key and get 57.99461679° which to the nearest degree is 58°

Edwin