Triangle ABC C = 90 ° AB = 12.5, BC = 12. Find the cosine of the outer angle at the vertex A.

The cosine of the inner angle (angle BAC) will be equal to the ratio of the adjacent leg to the hypotenuse. Those. cosBAC = CA / BA.
VA is known to us. We need to find the CA.
since triangle ABC is right-angled, then we can apply the Pythagorean theorem:
AB ^ 2 = BC ^ 2 + CA ^ 2
CA ^ 2 = AB ^ 2-BC ^ 2
CA ^ 2 = 12.5 ^ 2-12 ^ 2
CA ^ 2 = 156.25-144
CA ^ 2 = 12.25
CA = 3.5
cosBAC = CA / BA = 3.5 / 12.5 = 35/125 = 7/25 = 0.28
BAC is the inner corner. BAC and the outside angle at apex A are 180 degrees. Cosine can be 1 maximum.
This means that the cosine of the outer corner at the vertex A is 1-0.28 = 0.72
Answer: 0.72