SOLUTION: Is there a formula that can figure the lengths of the two legs of a right triangle given only the length of the hypotenuse and a ratio between leg a and b? such as: 'with length c

Click here to see ALL problems on Triangles

Question 753327: Is there a formula that can figure the lengths of the two legs of a right triangle given only the length of the hypotenuse and a ratio between leg a and b? such as:
'with length c (hypotenuse)=5 and the ratio between legs a and b being 4/3, figure the lengths of a and b' which, obviously in this case, is = to 3 and 4. But what about more complicated ones? like... say if the hypotenuse was 17 and the ratio between a and b is 2.5? Is it completely just trial and error, or is there a formula/expression to at least approximate the lengths to a couple of decimal places?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

I never actually saw such a thing, but there is no reason we can't derive such a formula.

Let the ratio of to be represented by , such that .

From this we can say

But we know that

Substituting:

Solve for

Then substitute back into to calculate the value of

In your example, presuming you mean that is to as 2.5 is to 1, then

so

And so on...

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it