Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
what exactly are x,y,r and $\theta$? – gfes Jun 6 '11 at 1:35
What are $y$, $r$, and $x$? And how is it you "know" $y$ and $r$? – Arturo Magidin Jun 6 '11 at 1:37
y is the opposite and r is the hypotenuse. – Adam Jun 6 '11 at 1:39
@Adam: Then you have a right triangle. Pythagoras is your friend (or should be, if you didn't keep snubbing him...) – Arturo Magidin Jun 6 '11 at 1:49
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. – Adam Jun 6 '11 at 1:50
up vote 2 down vote accepted

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 $x=4$.

share|cite|improve this answer

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.