In RT △ ABC, ∠ C = 90 °, a = 45 ° is known, AC: BC: ab

In RT △ ABC, ∠ C = 90 °, a = 45 ° is known, AC: BC: ab

If ∠ C = 90 ° and ∠ a = 45 ° can deduce ∠ B = 45, so BC = AC, ab = BC + AC = 2Ac, AC: BC: ab = 1:1: √ 2

In the triangle ABC, we know that angle B = 2, angle a, ab = 2CB

Take a point D on AB such that ACD = angle a, ad = CD, so angle CDB = 2 times angle a, because angle B = 2 times angle a, so angle CDB = angle B, so CD = CB, so ad = BC, because AB = 2BC = BC + BC, ab = ad + BD, so BD = BC, and because CD = BC, so CBD is equilateral triangle. So angle B = 60 degree, angle a = 30 degree, so angle c = 90

In the triangle ABC, angle B = 2, angle a, ab = 2BC, prove angle a = 30 degrees

Use sine theorem and trigonometric sum equal to 180 to do it. Try it by yourself. You will definitely do it. Believe in yourself!