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The problem provided involves a right triangle, where the angle of 30° and the adjacent side of 4 units are given. To solve for \( x \), the side opposite to the 30° angle, we can apply the **SOH** part of **SOHCAHTOA**, which relates sine to the opposite and hypotenuse:

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

Here, \(\theta = 30^\circ\), opposite = \( x \), and hypotenuse = 4. Given that \(\sin(30^\circ) = 0.5\), the equation becomes:

\[
0.5 = \frac{x}{4}
\]

Multiplying both sides by 4 to solve for \( x \):

\[
x = 0.5 \times 4 = 2
\]

So, \( x = 2 \).

Would you like more details or have any questions about this solution?

Here are 5 related questions you could explore:
1. How would you calculate the hypotenuse if the opposite side and angle were known?
2. What if the given angle was 45°, how would you calculate \( x \)?
3. How does SOHCAHTOA work for other trigonometric functions like cosine and tangent?
4. What would happen if the adjacent side and hypotenuse were given instead of opposite and adjacent?
5. How could you use the Pythagorean theorem to double-check the result?

**Tip:** Always verify which sides of the triangle are the opposite, adjacent, and hypotenuse based on the angle given.

Determine the value of x. Round your answer to one decimal place. Note: sin(30°) = 0.5, cos(30°) = 0.87, tan(30°) = 0.58

Learn how to find the value of the opposite side in a right triangle using trigonometric functions. Given the angle of 30° and adjacent side of 4 units, this problem shows how to apply the sine function.

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