# Can you find the the various values of a non

Can you find the the various values of a non 45-45- 90 triangle if only given hypotenuse and right angle?
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billyfcash5n
If $R$ is the circumradius, a is the length of the side and $A$ the opposite angle, you have
$\frac{a}{\mathrm{sin}A}=2R$
This relates also to the fact that in a fixed circle, the angle subtended by a chord is constant on each arc cut off by the chord.
Your problem is equivalent to "the angle in a semicircle is a right angle".
###### Not exactly what you’re looking for?
Frederick Kramer
That's precisely the idea; you can have different degrees of the angles that aren't the right angle, and these correspond to different side lengths (a la law of sines). This ultimately means that you can have infinitely many triangles for a given hypotenuse. Another way you can think of it is that we need the triangle to satisfy the Pythagorean Theorem: ${\overline{AB}}^{2}+{\overline{BC}}^{2}={\overline{AC}}^{2}$; we're given $\overline{AC}$, but if I choose any value less than for $\overline{AC}$ $\overline{AB}$, then I can solve for $\overline{BC}$, showing that there are infinitely-many solutions.