Solution:

∵ Sina = cosb > 0, where b is the interior angle of a triangle,

B is an acute angle.

∫cosB = sin(90-b)，sinA=cosB，

∴sinA=sin(90 -B)，

∴①∠A=90 -∠B，

∴∠A+∠B=90，

∴∠c = 90°, that is to say, this triangle is a right triangle.

②∠A= 180 -90 +∠B，

∴∠ A = 90+∠ B, A is an obtuse angle, and a triangle is an obtuse triangle.

Extended data

Sine law is a basic theorem in trigonometry, which points out that "in any plane triangle, the ratio of sine value of each side to its diagonal is equal and equal to the diameter of the circumscribed circle", that is, a/sinA = b/sinB =c/sinC = 2r=D(r is the radius of the circumscribed circle and D is the diameter).

As early as the 2nd century AD, Ptolemy, an ancient Greek astronomer, knew the sine theorem, and biruni (973- 1048), a famous Arab astronomer in the Middle Ages, also knew the sine theorem. However, it was the Arab mathematician and astronomer Nassir al-Ahldin who explicitly proposed and proved this theorem for the first time in the13rd century.

In Europe, the Jewish mathematician Gehlsen stated this theorem with sine, chord and arc: "In all triangles, the ratio of one side to the other is equal to the sine ratio of its diagonal", but he did not give a clear proof. /kloc-In the 5th century, the German mathematician Rejo Montanus gave the sine theorem in On Various Triangles, but simplified Nasir-Ud-deen's proof.

157 1 year, the French mathematician F. viete (1540-1603) proved the sine theorem in his laws of mathematics in a new way. Later, German mathematician B. Tix (15665438).