Let ABCD be a parallelogram with ∠BAC = 45° and ∠ABD = 30°.

What is the distance from B to diagonal AC in terms of the
lengths of sides AB and AD?

(In reply to Simple Trigonometry (spoiler) by Steve Herman)

Wow.   I didn't see it as quite so simple.

I instead solved by finding AO, then the area of triangle BAO, then working backwards from this triangle to find its altitude.

It turns out to be AB*sin(45º).
In general the distance is AB*sin(∠BAC)

∠ABD and the length of AD are not independent, nor are they so simple.

Posted by Jer on 2013-05-14 16:01:20