To solve this problem, we will use trigonometric ratios to find the angle ∠ABC. Since triangle ABC is a right triangle with a right angle at C, we can apply the sine, cosine, or tangent functions.

Given:

• $BC = 2.55$ cm (opposite side of ∠ABC)
• $AC = 5.89$ cm (adjacent side to ∠ABC)

We can use the tangent function because tangent of an angle in a right triangle is the ratio of the length of the opposite side to the adjacent side.

$\tan(\angle ABC) = \frac{BC}{AC} = \frac{2.55}{5.89}$

Let's calculate this ratio:

$\tan(\angle ABC) = \frac{2.55}{5.89} \approx 0.4324$

Next, we find the angle using the inverse tangent (arctan) function:

$\angle ABC = \tan^{-1}(0.4324)$

Now, let's calculate the angle.

$\angle ABC \approx \tan^{-1}(0.4324) \approx 23.4^\circ$

Rounding to the nearest degree:

$\angle ABC \approx 23^\circ$

Summary:

• ∠ABC is approximately 23°.

Would you like a detailed sketch of the triangle or any further explanation?

Here are some related questions you might find interesting:

1. What is the length of side AB using the Pythagorean theorem?
2. How would the value of ∠ABC change if side BC were longer?
3. What is the sine of ∠ABC?
4. What is the cosine of ∠ABC?
5. How would you find ∠ACB in this triangle?

Tip: When dealing with right triangles, always remember the basic trigonometric ratios: sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent).