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I've been surprised at how challenging this problem is. Given an isosceles trapezoid, with the larger base b, the four angles, and the two equal sides c know, find the length of the shorter base a. Is the calculation even possible without knowing the height?

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  • $\begingroup$ Clearly not; it depends on the angle the two equal sides make with the base. If the angle is close to zero, the remaining side is close to $b-2c$; if the angle is close to $\frac{\pi}{2}$, then remaining side is close to $b$. $\endgroup$
    – rogerl
    Commented Aug 21, 2015 at 14:25
  • $\begingroup$ what if the angles are known? $\endgroup$
    – nycguy92
    Commented Aug 21, 2015 at 14:50

2 Answers 2

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Trapezium$$a = b - 2 \,c \cos \alpha $$

where $ \alpha = $ angle between the big side and one of equal sides length $c$.

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The height can be between $0$ and $c$, and the side $a$ can be any value between $b-2c$ and $b$.

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  • $\begingroup$ So all that can be found are bounds? There's no definitive formula for base a? I find that surprising. After all, we know four angles and three sides of the geometry. That seems like a lot of information. $\endgroup$
    – nycguy92
    Commented Aug 21, 2015 at 14:48
  • $\begingroup$ Isoceles means the angles are the same, not what their value is. $\endgroup$
    – vonbrand
    Commented Aug 21, 2015 at 14:51
  • $\begingroup$ i edited the question so that the angles are know. if the angles are know, then is there some formula for a? $\endgroup$
    – nycguy92
    Commented Aug 21, 2015 at 14:52

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