To find the value of \(\sec B\) in the given right-angled triangle, we need to first understand the trigonometric properties of the triangle.

In a right-angled triangle:

• The side opposite the right angle is the hypotenuse.
• The sides forming the right angle are the adjacent and opposite sides, relative to the angle being considered.

Given:

• The triangle is right-angled at \(A\).
• \(BC = 5.2\, \text{cm}\) (this is the hypotenuse, since it is opposite the right angle at \(A\)).
• \(AB = 3\, \text{cm}\) (this is one of the sides adjacent to angle \(B\)).

We need to find \(\sec B\), which is defined as:

\(\sec B = \frac{\text{Hypotenuse}}{\text{Adjacent side to } B} = \frac{BC}{AB}\)

Substituting the known values:

\(\sec B = \frac{5.2}{3}\)

Calculating this gives:

\(\sec B = 1.7333\ldots\)

Rounding this to two decimal places, we find:

\(\sec B \approx 1.73\)

Therefore, the correct answer is 1.73.

This calculation matches the option 1.73, confirming it is correct.