In triangle ABC, angle C is 90 degrees sin A = 2√2 / 5 find the cosine of the angle at the vertex A.

First you need to draw a right-angled triangle ABC with a right angle C. Then write Given: sinA = 2 √2 / 5. Next, write Find: cosA -? Now we write the solution:
1) sine is the ratio of the OPPOSITE angle to the hypotenuse, hence the hypotenuse AB = 5 and the leg opposite the angle A (CB) = 2√2.
2) By the Pythagorean theorem, we find the missing leg: we get √17. (now we can find the cosine of the angle A)
3) cosine is the ratio of the ADJUSTING leg to the hypotenuse, i.e. AC / AB. We get √17 / 5