perplexus.info :: Geometry : Distance to Diagonal

Distance to Diagonal (Posted on 2013-05-14)

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?

See The Solution Submitted by Bractals

Rating: 3.0000 (1 votes)

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Simple Trigonometry (spoiler)

| Comment 1 of 6

Drop a perpendicular from point B to line AC. Call the point of intersection E.

Then triangle ABE is an isosceles right triangle, with hypotenuse = length(AB). The requested distance is the length of BE, which is just length(AB)/sqrt(2). Final answer.

We do not need to know ∠ABD or the length of AD, although I suspect that the two are not independent.

Posted by Steve Herman on 2013-05-14 15:13:53

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