Given the right trapezoid calculate angle theta and the area of triangle hat(EAD), provided EA=4, AB=BC=CD=DA=2, AB_|_EC?

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1 Answer
Jul 11, 2016

/_theta = arctan((sqrt(3)-1)/2)~~0.350879411 rad

S_(EAD) = 2

Explanation:

From right triangle Delta ABE, knowing hypotenuse AE=4 and cathetus AB=2 we can find another cathetus:
BE=sqrt(4^2-2^2)=sqrt(12)=2sqrt(3).

In the right triangle Delta DCE cathetus CD=2. Second cathetus CE = CB+BE = 2+2sqrt(3)

Now we can determine tangent of angle /_ theta:
tan(theta) = (CD)/(CE) = 2/(2+2sqrt(3)) = 1/(sqrt(3)+1)=(sqrt(3)-1)/2
Angle /_theta can be determined using an inverse function tan^(-1)() or, as it is often expressed, arctan():
/_theta = arctan((sqrt(3)-1)/2)~~0.350879411 rad

Area of triangle Delta EAD can be calculated using the length of its base AD and altitude DC:

S_(EAD) = 1/2*AD*DC = 1/2*2*2 = 2