In a right-angled triangle ABC, the angle is C = 90 °. Find leg length AC if angle B = 45 ° and leg BC = 19.

It is known from the condition that in a right-angled triangle ABC the angle C is 90 °. We need to find leg length AC if angle B is 45 ° and leg length BC = 19.
Let’s consider a triangle ABC.
AC and BC are the legs of a right triangle, and AB is the hypotenuse.
Let’s find the degree measure of the third angle of the triangle. Based on the fact that the sum of the angles of the triangle is 180 °, we get:
180 ° – (90 ° + 45 °) = 180 ° – 135 ° = 45 °.
We got an isosceles triangle, since the two angles are 45 ° each.
Based on this, we get:
AC = BC = 19.