To solve for $\sec A$ in the right triangle, we need to understand the following:

In a right triangle, the secant ($\sec$) of an angle is defined as the ratio of the hypotenuse to the adjacent side of the angle.

Given Data:

• Hypotenuse = $5$
• Adjacent side to angle $A$ = $4$

Solution:

$\sec A = \frac{\text{Hypotenuse}}{\text{Adjacent side}} = \frac{5}{4}$

Thus, the correct answer is: $\sec A = \frac{5}{4}$

Would you like a detailed explanation on how secant relates to other trigonometric functions, or do you have any other questions?

Follow-up Questions:

1. How would you find $\cos A$ in this triangle?
2. What would be $\sin A$ for this triangle?
3. Can you calculate $\tan A$ using the given sides?
4. How would you find $\csc A$ if needed?
5. Is it possible to find angle $A$ in degrees?

Tip:

Remember, $\sec$ is the reciprocal of $\cos$. So, $\sec A = \frac{1}{\cos A}$. This relationship can simplify your calculations when dealing with trigonometric functions.