Find *x* rounded to one decimal place.
angle 30 degree traingle and opposite 3 

To find the length of the side \( x \) in a right triangle where the angle is \( 30^\circ \) and the opposite side is 3 units, you can use the trigonometric sine function. The sine function is defined as:

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

Given:
- Angle \( \theta = 30^\circ \)
- Opposite side = 3 units
- \( x \) = hypotenuse (which we need to find)

The sine function becomes:

\[
\sin(30^\circ) = \frac{3}{x}
\]

Since \( \sin(30^\circ) = 0.5 \), we have:

\[
0.5 = \frac{3}{x}
\]

Now, solve for \( x \):

\[
x = \frac{3}{0.5} = 6
\]

So, the hypotenuse \( x \) is 6 units.

Would you like more details or have any other questions?

Here are some related questions:
1. How do you find the other sides of the triangle using trigonometric functions?
2. What if the angle was \( 45^\circ \) instead of \( 30^\circ \)?
3. How would the problem change if you were given the hypotenuse instead?
4. Can you use the cosine function to find another side of the triangle?
5. What is the area of the triangle in this scenario?

**Tip:** In a 30-60-90 triangle, the hypotenuse is always twice the length of the side opposite the \( 30^\circ \) angle.

Learn how to find the length of side x in a right triangle with a 30 degree angle and opposite side of 3 units using trigonometric sine function. Explore step-by-step solution and related concepts in trigonometry. Suitable for high school students.

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