Right triangle given hypotenuse and one side?

Hi fellas!
I'm working on a really large and complex model and I've come across with what, at first, may seem a easy problem.
Well, I'm trying to draw a right triangle from the hypotenuse and one side, but I know no angles (except the 90º one, of course).
I've tried to draw a circle with the known side as the radius, with the center on one end of the hypotenuse and then draw a line from the other end tangent to the circle, but this method is slow and inaccurate.
Then I drew a random right triangle and by using pythagoras theorem scale it on the second side axis, but I'd have to do this 73 times in the model and I'd go crazy...Do you know any plugin or easier way to solve this?
Thank you in advance,
C.

Trigonometry works for me.
Or how about this?
This could be done graphically with Fredo's Rotate tool in the FredoScale suite.

Nice solution, Dave.

Thank you sir.

Dave, you omitted to mention that the third side is first constructed perpendicular to the other one. Same question and a similar answer were posted on SketchUp Community  great minds! The method posted there uses only the builtin arc tools not Fredo's, but requires an extra step or two.

It was an intentional omission. I figured it was clear enough given the topic of the thread. The method would work for nonright triangles as well. Of course a nonright triangle doesn't have a hypotenuse.

As nice a solution as Dave's is I think with 73 of them you'd be faster doing the calc for the third side, (very simple with Dave's calculator link), then simply draw 73 rectangles with the two dimensions and split them on the diagonal.
You need to go a few decimal places or you'll be out by a few mm over several m. 
Good point, Box. I thought the 73 times things was number of tries to get it right.

You might be right, I often confused Trombones with Virgins. Hang on now that was 76 of one and 4 n 20 of the other.......I guess the 73 triangles are in the percussion section

What about the blackbird pie?

Hi dear SketchUppers,
A second solution which gives the same result
This alternative way is a bit longer to achieve because you need to delete the circle and clean cpoints and clines, but this ancient TIG's set of tools although poorly known can bring great services.The plugin used is TIG's TrueTangents v3.0
The tool used is True Intersections.
http://sketchucation.com/forums/viewtopic.php?p=160780#p160780
http://sketchucation.com/pluginstore?pln=TrueTangents
Cheers,
Simon
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