In triangle ABC, angle C is 90 degrees, AB = 75, BC = 45. Find cos A.

ABC is a right-angled triangle. To find the AC leg, we use the Pythagorean theorem (the square of the unknown leg is equal to the difference between the square of the hypotenuse and the square of the second leg):

AC ^ 2 = AB ^ 2 – BC ^ 2 = 75 ^ 2 – 45 ^ 2 = 5625 – 2025 = 3600;

AC = √3600 = 60;

The cosine of an acute angle of a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse: cos A = AC / AB = 60/75 = 4/5.

Answer: 4/5.