Can you provide an example of finding sine

Absolutely! Let's go through a concrete example to find the sine of an angle in a right triangle.

### Example Problem

Imagine you have a right triangle where:
- The hypotenuse is 10 units long.
- The side opposite the angle \( \theta \) is 6 units long.

### Step 1: Identify the Sides
- **Hypotenuse**: 10 units
- **Opposite side**: 6 units
- The adjacent side isn't needed to find the sine, so we can ignore it for now.

**Question 1**: Can you confirm which side is the hypotenuse and which is the opposite side in this triangle?

### Step 2: Write Down the Sine Formula
The sine of an angle \( \theta \) is given by:

\[
\sin(\theta) = \frac{{\text{{opposite}}}}{{\text{{hypotenuse}}}}
\]

### Step 3: Plug in the Values
Now, substitute the lengths of the opposite side and the hypotenuse into the formula:

\[
\sin(\theta) = \frac{6}{10}
\]

### Step 4: Simplify the Fraction
Simplify the fraction to make the calculation easier:

\[
\sin(\theta) = \frac{6}{10} = 0.6
\]

So, the sine of the angle \( \theta \) is 0.6.

**Question 2**: Does this process make sense to you? What would you do if the opposite side were 5 units and the hypotenuse were 13 units?

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Do you want to go over any particular part of this example in more detail, or do you have any other questions? Here are 5 related questions to consider:

1. How would you find the sine if you were given the angle but not the side lengths?
2. What happens to the sine value if the opposite side increases but the hypotenuse stays the same?
3. If the hypotenuse were 20 units and the opposite side were 12 units, what would the sine of the angle be?
4. How can you use the sine value to find the length of the opposite side if you know the hypotenuse?
5. Is it possible for two different angles in different triangles to have the same sine value? Why?

**Tip**: Always check if you can simplify the fraction when finding the sine—it makes your calculations cleaner and easier to understand!

Learn how to find the sine of an angle in a right triangle with a detailed example problem. Understand the sine formula and its application using specific side lengths. Suitable for high school students studying trigonometry.

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