0
$\begingroup$

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?

$\endgroup$
2
  • $\begingroup$ 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 Aug 21 '15 at 14:25
  • $\begingroup$ what if the angles are known? $\endgroup$ – nycguy92 Aug 21 '15 at 14:50
2
$\begingroup$

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

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

$\endgroup$
0
$\begingroup$

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

$\endgroup$
3
  • $\begingroup$ 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 Aug 21 '15 at 14:48
  • $\begingroup$ Isoceles means the angles are the same, not what their value is. $\endgroup$ – vonbrand Aug 21 '15 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 Aug 21 '15 at 14:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.