Find all values.

skeeter

Math Team
Jul 2011
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Texas
Not gonna lie I don't fully understand what you're saying here
option 2 ... (refer to the attached diagram)

$\dfrac{A}{3} < \dfrac{1}{2} ab \sin{\theta} < \dfrac{A}{2}$

solve the inequality for the length of $\color{red}a$

$A = \text{ area of quadrilateral ABCD}$

$\theta = \angle{DAB}$

$b = |AB|$
 

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Mar 2019
196
1
TTF area
I got length a to = 147.433 so 147 length opposite angle A =88.58 so 89 and angle A/theta = about 30.631degrees so 31degrees?


Edit: For the part before Line DX=45
 
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skeeter

Math Team
Jul 2011
3,364
1,855
Texas
To review the question from the previous page ...

The second part is..... they want to build a new fence across line ABCD. The fence will start at point B and connect with the existing line AD. The new fence will then divide the field into a triangular section, towards the north, and a quadrilateral section, towards the south. They want the area of the triangular section to be between a third and half of the area of the whole field .
See attached diagram ...
 

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Mar 2019
196
1
TTF area
Since they want the area of the triangular section to be between a third and half of the area of the whole field . Do I just pick a length between 53.68 and 80.52?