$17 \cdot 177$ Let the two legs of a right triangle be $a, b$, the hypotenuse be $c$, and the altitude to the hypotenuse be $h$. Then, the shape of the triangle formed by $c+h, a+b, h$ as sides is
(A) a right triangle.
(B) an acute triangle.
(C) an obtuse triangle.
(D) cannot be determined, the shape depends on the sizes of $a, b, c$.
(Chinese "Zu Chongzhi Cup" Junior High School Mathematics Invitational Competition, 1989)
[Solution] According to the Pythagorean theorem, we have $a^{2}+b^{2}=c^{2}$, and the area of the triangle is
$$
S=\frac{1}{2} a b=\frac{1}{2} c h .
$$

Then
$$
(c+h)^{2}=c^{2}+2 c h+h^{2} \text {. }
$$

Also, $(a+b)^{2}=a^{2}+2 a b+b^{2}=a^{2}+2 c h+c^{2}-a^{2}=c^{2}+2 c h$.
$\therefore$
$(c+h)^{2}=(a+b)^{2}+h^{2}$.

Thus, the newly formed triangle is a right triangle.
Therefore, the answer is $(A)$.