# Find the height of any triangle?

1. Oct 10, 2011

### moonman239

1. The problem statement, all variables and given/known data

I have the side lengths of a triangle. The base is 190 ft long, side A is 182 ft long and side B is 363 ft long. That's all I know.

2. Relevant equations

3. The attempt at a solution

I know these side lengths are related somehow.

2. Oct 10, 2011

### iRaid

I'm not 100% sure this is the formula, but try this:
$h=\frac{2}{c}\sqrt{s(s-a)(s-b)(s-c)}$
where
$s=\frac{a+b+c}{2}$

3. Oct 10, 2011

### ArcanaNoir

Draw the picture, use the law of sines or cosines to find the angle measures, drawn an altitude, calculate.

4. Oct 11, 2011

### verty

Or you could use the fact that you know the distance of the apex from the other two corners to find two equations in x and y.

5. Oct 11, 2011

### SammyS

Staff Emeritus
Use the law of cosines to find the angle opposite side B first.

6. Oct 11, 2011

### phinds

DRAW THE DAMN PICTURE. All of the other suggestions here are good but if you don't start off by drawing a reasonable picture of what you're working with, you're shooting in the dark.

7. Oct 11, 2011

### SammyS

Staff Emeritus
Very true !!!