Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given a trapezoid like the one shown below, how do I determine the length of the wider base? I'm looking for a formula based method rather than drawing the shape and measuring it.

Sides of a Trapazoid

share|cite|improve this question
up vote 2 down vote accepted

Use the Law of Sines on the triangles (separately) on either end.

For example, on the right side of the trapezoid, drop a perpendicular from the top right vertex. Call the length of the base of the resulting right triangle $x$. The other (non-hypotenuse) side is 3/4. The bottom (interior) angle is $70^\circ$ while the top (interior) angle is $20^\circ$.

The Law of Sines says $${{3\over 4}\over \sin(70^\circ)}={x\over \sin(20^\circ)}.$$ Solve for $x$ to obtain $x={3\over 4}\cdot{\sin(20^\circ)\over \sin(70^\circ)}\approx 0.272978$.

Play the same game on the other side and you will know the total length of the base of the trapezoid.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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