Unknown lengths of triangle, known area and internal angles

[tim9000]

Homework Statement

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!

Homework Equations

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

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.

 

[pasmith]

Homework Statement

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?

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

 

[HallsofIvy]

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.

 

[tim9000]

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

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

 

[tim9000]

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.

Wow, that's brilliant, thanks very much!