Lg sin B = -lg radical number 2 = lg( 1/ radical number 2), that is, sin B = 1/ radical number 2, and because b is an acute angle, b = 45.

Lga-lgc =lg (a/c)= lg( 1/ root number 2), so a/c= 1/ root number 2. Let a=k, then c=k* radical 2. According to the cosine theorem, cosB=(a +c -b).

Therefore, a triangle is an isosceles right triangle.