Answer:
5/13
Step-by-step explanation:
From the mnemoic SOH CAH TOA, we know that ...
... Cos = Adjacent/Hypotenuse
In this triangle, that means ...
... cos(A) = AC/AB
We are given the value of AC, but we need to find the value of AB. We can do that using the Pythagorean theorem:
... AB² + AC² +BC²
... AB² = 15² +36² = 1521 = 39²
... AB = 39
Then ...
... cos(A) = 15/39 = (5·3)/(13·3)
... cos(A) = 5/13
