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To calculate the measure of \( \theta \) in the triangle to the nearest degree, we can use trigonometric functions. Here's the process:

### Step 1: Identify the sides of the triangle relative to \( \theta \)
- Opposite side: 45 cm
- Hypotenuse: 71 cm

We will use the sine function, as it relates the opposite side and the hypotenuse:
\[
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}
\]

### Step 2: Substitute the known values
\[
\sin(\theta) = \frac{45}{71}
\]

### Step 3: Calculate the sine value
\[
\sin(\theta) \approx 0.6338
\]

### Step 4: Find \( \theta \) using the inverse sine function
\[
\theta = \sin^{-1}(0.6338)
\]

Using a calculator:
\[
\theta \approx 39^\circ
\]

### Final Answer:
\[
\theta \approx 39^\circ
\]

Would you like further details or explanations about any step? 

### Related Questions:
1. How do you calculate the other angle in the triangle?
2. What other trigonometric functions could be used here, and why?
3. How would this change if the triangle were not a right triangle?
4. Can you use cosine or tangent to verify this result?
5. What is the significance of rounding to the nearest degree in practical problems?

### Tip:
Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems involving angles.

Calculate the measure of \( \theta \) in the triangle to the nearest degree, where the opposite side is 45 cm and the hypotenuse is 71 cm.

Learn how to calculate the angle \( \theta \) in a right triangle with opposite side 45 cm and hypotenuse 71 cm using the sine function. This step-by-step guide includes the use of trigonometric functions, inverse sine, and rounding to the nearest degree. Suitable for students in Grades 8-10.

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