# Thread: Finding side on triangle

1. ## Finding side on triangle

Find x

2. 6 what? Degrees? 15 degrees? 200 what? Meters? Maybe they didn't give you any units. That's ok.

What have you thought of doing so far?

3. 6 and 15 are degrees and the 200 has no units.

I've found all angles on the triange and don't know where to go from there

4. I would slap a label on the segment of the horizontal just to the right of the 200. What do you want to call that?

Further question: are we right in assuming the lower-right angle is a right angle?

5. Yes. The lower right is a right angle. I named the segment to the right of 200 'y' and the hypotenuse 'z'

6. Great. Now, just thinking out loud here. You could use the Pythagorean theorem, since you have a right triangle. The only problem with that is that it introduces yet another variable for which you'd need another equation. What's a relevant, correct equation you could write down that involves x?

7. I tried sin cos and tan for the bottom left hand corner angle (6 degrees) and the angle at the top (84 degrees) and tried to equate some of the equations that involved x but hasn't worked out so far.

8. Ok, well, show me what you have so far. We'll go from there.

9. $sin 6 = \frac{x}{2}$

$cos 6 = \frac{200+y}{z}$

$tan 6 = \frac{x}{200+y}$

$sin 84 = \frac{200+y}{z}$

$cos 84 = \frac{x}{z}$

$tan 84 = \frac{200+y}{x}$

10. Of those equations, I would agree with all but the first one.

You're going to need some equations having to do with the inner triangle, or I'm mistaken. What can you get from the inner triangle?

11. Oh, and a LaTeX hint or two: use \cos instead of cos. Also, I find it a good idea always to put parentheses around the argument. Thus, $\sin(6^{\circ})$, not $\sin 6^{\circ}$. The reason is that sometimes, the arguments get to be pretty hairy, and you can get some ambiguous expressions. It's better to be safe!