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The given triangle is a right triangle with one side labeled \( s \), a hypotenuse of 14 units, and an angle \( t = 30^\circ \).

To solve for \( s \), we can use the trigonometric sine function. In a right triangle:

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

In this case, the angle \( \theta = 30^\circ \), the opposite side is \( s \), and the hypotenuse is 14. Therefore, we have:

\[
\sin(30^\circ) = \frac{s}{14}
\]

Since \( \sin(30^\circ) = 0.5 \), we substitute this value into the equation:

\[
0.5 = \frac{s}{14}
\]

Now, solving for \( s \):

\[
s = 0.5 \times 14 = 7
\]

So, the exact value of \( s \) is \( \boxed{7} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the cosine of a 30-degree angle in this triangle?
2. How do you calculate the other side of the triangle using trigonometry?
3. What are the properties of a 30-60-90 triangle?
4. Can you find the area of the triangle if one side is known?
5. What happens if the hypotenuse changes while keeping the angle the same?

**Tip:** In a 30-60-90 triangle, the sides follow a specific ratio: 1 (opposite 30°), \( \sqrt{3} \) (opposite 60°), and 2 (hypotenuse).

Find the exact value of the side s in the triangle below. The angle t, noted in blue, measures 30°.

Learn how to find the exact value of side 's' in a right triangle where the hypotenuse is 14 units and the angle is 30°. This problem uses trigonometry concepts like the sine function and properties of special triangles.

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