26. It is known that in a right-angled triangle \(c^{2}=a^{2}+b^{2}\), where \(a\) and \(b\) are the lengths of the legs; \(c\) is the length of the hypotenuse. Find the acute angles of the triangle if \(\left(\frac{c}{a+b}\right)^{2}=0.5\).
26. Solution. From the given equality, it follows that \(2 c^{2}=\) \(=(a+b)^{2}\), therefore,

\(2\left(a^{2}+b^{2}\right)=a^{2}+2 a b+b^{2} ;(a-b)^{2}=0, a=b\),

hence the given right triangle is isosceles, and each of its acute angles is \(45^{\circ}\).