In triangle ABC, angle C = 90 degrees, AB = 55, BC = 33. Find cosine A.

The cosine of an angle in a right-angled triangle is the ratio of the adjacent leg to the hypotenuse. In our case:
Cos A = AC / AB.
The adjacent leg of the AC is unknown, we find it using the Pythagorean theorem:
AC = √ (AB² – BC²) = √ (55² – 33²) = √ (3025 – 1089) = √1936 = 44.
Let’s find what the cosine of the angle A is equal to:
Cos A = AC / AB = 44/55 = 4/5 = 0.8.
Answer: the cosine of angle A is 0.8.