Hypotenuse of 15 and opposite of 12for this triangle what is the cos

right triangle with side "a" = 12 and hypotenuse "c" = 15

cos(∠A)

The Pythagorean theorem tells you

... b = √(c² - a²) = √(225 - 144) = √81 = 9

The definition of the cosine tells you

... cos(A) = b/c = 9/15

... cos(A) = 3/5 . . . . . . reduce the fraction

ABC = XYZ  by  SAS

AB = XY    -     Side

A = X         -    Angle

So you want to find another congruent side.

Removing the taken possible side, two sides can be congruent.

Either :

BC = YZ

OR

AC = XZ