A quadrilateral contains two equal sides measuring 12 cm each and an included right angles. If the measure of the third side is 8 cm and the angle opposite the right angle is 120, find the measure of the fourth side and the area of the quadrilateral.

Question

mathstudent55 · Answer

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ranga · Answer

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ranga · Answer

You can find AC from the right triangle ADC.

Assume BC = x.  You can use the law of cosines to to find AC in terms of x.

Equate the above two equations and solve for x.

ranga · Answer

AC^2 = AD^2 + DC^2 = 12^2 + 12^2 = 288  -------- (1) 
AC^2 = AB^2 + x^2 - 2AB(x)cos(120) 
         = 8^2 + x^2 - (2)(8)(x)cos(120) 
         = 64 + x^2 + 8x 
AC^2 = x^2 + 8x + 64   ----------- (2) 

Equate (1) and (2) and solve for x

directrix · Answer

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