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In the given triangle, we are tasked with finding the value of \(x\), which represents the hypotenuse, using the trigonometric ratio.

We are given:
- The opposite side to the angle \(35^\circ\) is \(20\) cm.
- The hypotenuse is labeled as \(x\) cm.

We can use the sine trigonometric function since we have the opposite side and need to find the hypotenuse:

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

Substituting the known values:

\[
\sin(35^\circ) = \frac{20}{x}
\]

Now, we solve for \(x\):

\[
x = \frac{20}{\sin(35^\circ)}
\]

Let me calculate the value of \(x\).The value of \(x\), the hypotenuse, is approximately \(34.87\) cm.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. How would you calculate the adjacent side using trigonometry in this triangle?
2. What other trigonometric ratio could be used to solve for \(x\)?
3. How does the value of \(x\) change if the angle is increased or decreased?
4. What is the relationship between the sides of a right triangle and the Pythagorean theorem?
5. How can you apply the sine rule in non-right-angled triangles?

**Tip:** Always remember to check if the triangle is a right triangle before using basic trigonometric functions like sine, cosine, or tangent.

Work out the value of x, where the opposite side is 20 cm and the angle is 35 degrees.

Learn how to calculate the hypotenuse of a right-angled triangle given a 35° angle and an opposite side of 20 cm. Using the sine function, the hypotenuse is approximately 34.87 cm. This problem covers core trigonometric concepts and is suitable for students in Grades 9-10.

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