Answer:

Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. Since the hypotenuse is in the ratio of 5 to 3, we can write:

c = 5x (where x is a constant of proportionality)

and

b = 3y

a = 4y (since the triangle is bisected, we can use the Pythagorean triple 3-4-5)

We can use the Pythagorean theorem to find x, y, and c:

a^2 + b^2 = c^2

(4y)^2 + (3y)^2 = (5x)^2

16y^2 + 9y^2 = 25x^2

25y^2 = 25x^2

y^2 = x^2

Since y and x are positive, we can take the square root of both sides to get:

y = x

Now we can substitute y = x into our expressions for a and b:

a = 4y = 4x

b = 3y = 3x

So the two legs of the right triangle are in the ratio of 4 to 3. Therefore, the acute angles of the triangle are:

arctan(4/3) and arctan(3/4)

Using a calculator, we can find that these angles are approximately 53.13 degrees and 36.87 degrees, respectively.