In triangle ABC, angle C is 90 degrees. AC = 5, sinA = 2 / √5. Find BC.

Let’s use the basic trigonometric identity and write it down for angle A:
cos² A = 1 – sin² A;
cos A = √ (1 – sin² A) = √ (1 – 4/5) = √1 / 5 = 1 / √5 = √5 / 5.
Let’s write the definition of the cosine for angle A:
cos A = AC / AB. From here we find the hypotenuse AB:
AB = AC / cos A = 5 / √5 / 5 = 5√5.
We find the leg BC by the Pythagorean theorem:
BC = √ (AB² – AC²) = √ (125 – 25) = √100 = 10.
Answer: the BC leg is 10.