Answer:
[tex]\boxed{6}[/tex]
Step-by-step explanation:
We can use the geometric mean theorem:
The altitude on the hypotenuse is the geometric mean of the two segments it creates.
In your triangle, the two segments are MP and PO.
MP + PO = MO
MP + 3 = 15
MP = 12
Then,
[tex]h = \sqrt{12 \times 3} = \sqrt{36} = \mathbf{6}\\\text{The altitude of the triangle is }\boxed{\textbf{6}}[/tex]
