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Finding exact values for trig functions of acute angles.

I have $\sin \theta = 3/5$.

I know that $y = 3$ and $r = 5$.

How the heck do I get $x$ if I don't know the angle?

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    Its been 8 years or so since I have had to us it so it is easy to forgot. That or am an an idiot.2011-06-06

2 Answers 2

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If you know that $y=3$ and $r=5$, then because (presumably) the triangle is a right triangle with legs of length $x$ and $y$, and hypotenuse $r$, by the Pythagorean theorem we have that $x^2+y^2=r^2,$ hence $x^2+9=25.$ Thus $x^2=16$, and therefore $x=4$.

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You can draw a picture, too. That makes keeping things straight easy.