We are given a right-angled triangle $ABC$, where:

• $AB = 3.5 \, \text{cm}$
• $BC = 2.3 \, \text{cm}$
• $\angle B = 90^\circ$

We need to find $\angle C$ correct to one decimal place.

Since the triangle is right-angled at $B$, we can use trigonometric ratios to find $\angle C$. The tangent of angle $C$ is the ratio of the opposite side to the adjacent side.

$\tan(\angle C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB}$

Substituting the values:

$\tan(\angle C) = \frac{2.3}{3.5}$

Now, let's calculate this and find the angle $C$.The angle $\angle C$ is approximately $33.3^\circ$, correct to one decimal place.

Let me know if you need further details or clarifications.

Here are 5 related questions to expand your understanding:

1. How would you find $\angle A$ using the information given?
2. What is the sine of $\angle C$ based on the triangle's dimensions?
3. How can you calculate the hypotenuse of the triangle using the Pythagorean theorem?
4. What other trigonometric ratio could you use to find $\angle C$?
5. How would you solve for $\angle C$ if only the hypotenuse was given?

Tip: Always remember to check that your calculator is in the correct mode (degrees or radians) when working with angles!