# Unknown lengths of triangle, known area and internal angles

1. Nov 4, 2013

### tim9000

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

I know the area of a right angled triangle, I also know the ratio of the two non-hypotenuse sides.
Is there anyway of finding the lengths?

Thanks!

2. Relevant equations

I don't think there are any like Area = 1/2abSinC

3. The attempt at a solution

I obviously know that tan of the ratio will give one angle, so I know the internal angles.

buggered if I know, it's 2:45am here.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 4, 2013

### pasmith

If the sides are $a$ and $b$ then you know that the area of the triangle is $\frac12 ab$.

3. Nov 4, 2013

### HallsofIvy

Staff Emeritus
If you call the two legs a and b then the area is (1/2)ab= A so ab= 2A.
The ratio of the two sides is a/b= r so that a= br. Replace a in the first equation by that: ab= (br)b= rb^2= A so b^2= A/r. Solve for b, then solve for a.

4. Nov 4, 2013

### tim9000

I DON'T know the sides, just the ratio of the sides (the gradient of the hypotenuse)

5. Nov 4, 2013

### tim9000

Wow, that's brilliant, thanks very much!