The problem in the image asks to find a decimal approximation for the secant of $50^\circ 24'$.

Here’s how to approach it:

1. Convert the angle to decimal degrees: $50^\circ 24' = 50^\circ + \frac{24}{60}^\circ = 50^\circ + 0.4^\circ = 50.4^\circ$

2. Find the secant of the angle: The secant function is the reciprocal of the cosine function: $\sec(\theta) = \frac{1}{\cos(\theta)}$ So, we need to compute: $\sec(50.4^\circ) = \frac{1}{\cos(50.4^\circ)}$

Let me calculate that value for you.The decimal approximation of $\sec(50^\circ 24')$ is approximately 1.5688145, rounded to seven decimal places.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you convert degrees and minutes to decimal degrees?
2. What is the difference between secant and cosine functions?
3. How is the secant function used in real-world applications?
4. Can the secant function ever have a value less than 1?
5. How does the secant function behave as the angle approaches 90°?

Tip: Always ensure your calculator is in degree mode when dealing with trigonometric functions involving degrees!