That’s interesting because, as @DaveR noted earlier, without some additional information the question is ill-posed in the sense that there are infinitely many possible solutions. Math can’t overcome that! I suppose your way, like what he showed, would be arbitrarily choosing a particular one of them?
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I’m reminded of one of my favorite questions posed on a PBS show decades ago: How long is a piece of string?
Shep
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Oh, but that one’s easy: the distance from one end to the other 
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twice as long as half of it…
john
Of course with an angle given between the base and the 9 in. side, the rest could be derived.
(@slbaumgartner and @john_drivenupthewall)… you both nailed it.
Took me hours to figure out the answer with math.
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Just need a bit of String theory.
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draw a pentagon, then explode it. then just scale each side to length. How easy is that? And I am not even a sketchup Guru