We are tasked with finding the measure of $\angle B$ in a right triangle where:

• The opposite side to $\angle B$ is $5 \, \text{cm}$.
• The hypotenuse is $10 \, \text{cm}$.

We can use the sine function:

$\sin(\angle B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{10} = 0.5$

Now, take the inverse sine ($\sin^{-1}$) to find $\angle B$:

$\angle B = \sin^{-1}(0.5) = 30^\circ$

So, the measure of $\angle B$ is 30 degrees.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions for practice:

1. How do you calculate the angle if the adjacent side and hypotenuse are given?
2. What trigonometric ratio involves the opposite side and adjacent side?
3. What is the cosine of $\angle B$ in this triangle?
4. Can you find the measure of $\angle A$ in this triangle?
5. What are some practical applications of trigonometry in real-world scenarios?

Tip: Always double-check the trigonometric function used based on the given sides (opposite, adjacent, or hypotenuse).