Given right triangle abc with altitude cd find ad ab and dc

Assuming the vertex is at c, The Pythagorean theorem tells you

... ab = √ (ac^2 + bc^2)

Because all the triangles are similar,

... cd/bc = ac/ab

... cd = ac*bc/√ (ac^2 + bc^2)

Likewise,

... ad/ac = ac/ab

... ad = ac^2/√ (ac^2 + bc^2)

Your segments are

... ad = ac^2/√ (ac^2 + bc^2)

... ab = √ (ac^2 + bc^2)

... dc = ac*bc/√ (ac^2 + bc^2)