Question 1209009
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Farmer Jessie has a field shaped as quadrilateral ABCD. She measures three of the sides 
AB = 50 meters, BC = 65 meters, and CD = 80 meters. She also determines 
that angle ABC = 130 degrees and BCD = 52 degrees.
(a) What is the distance between points A and C?
(b) Show one way to find the area of triangle ABC.
(c) Show a different way to find the area of triangle ABC.
(d) What is the area of quadrilateral ABCD?
Round each result to 3 decimal places.
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(a)  Use the cosine law formula for triangle ABC

        AC = {{{sqrt(50^2 + 65^2 - 2*50*65*cos(130^o))}}} = {{{sqrt(6725 - 2*50*65*(-0.64278760968))}}} = 104.418 meters  (rounded).    <U>ANSWER</U>



(b)  Use the formula for the area of a triangle

        {{{area[ABC]}}} = {{{(1/2)*AB*BC*sin(ABC)}}} = {{{(1/2)*50*65*sin(130^0)}}} = {{{(1/2)*50*65*0.76604444311}}} = 1244.822 m^2  (rounded).    <U>ANSWER</U>
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(a) &nbsp;and &nbsp;(b) &nbsp;are solved.