Final answer:
The approximate value of θ when cos(θ) = 7/9 is found using the inverse cosine function, which gives us approximately 38.94°. Hence, the closest answer is θ = 38°.
Step-by-step explanation:
The question asks for the approximate value of θ if cos(θ) = 7/9. To solve this, we can use a calculator to find the inverse cosine (also known as arccos). When we input arccos(7/9) into a calculator, we find that θ is approximately 38.94°. The nearest degree to that would be 38°. Therefore, the closest answer from the given options is a. θ = 38°.