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This is a right-angled triangle with the given sides:

- Opposite side to angle \(x^\circ\) = 3.9 cm
- Hypotenuse = 4.7 cm

To find \(x\), we use trigonometry, specifically the sine function:

\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3.9}{4.7}
\]

First, calculate the sine:

\[
\sin(x) = \frac{3.9}{4.7} \approx 0.8298
\]

Next, we find the angle \(x\) by taking the inverse sine (arcsin):

\[
x = \sin^{-1}(0.8298)
\]

Using a calculator:

\[
x \approx 56.3^\circ
\]

So, the value of \(x\) is approximately **56.3°** (correct to 1 decimal place).

Would you like further clarification or more details?

Here are 5 related questions to expand on this concept:

1. How would you calculate the length of the adjacent side using trigonometry?
2. Can you use cosine or tangent to solve for \(x\) in this triangle?
3. How does the Pythagorean theorem relate to this problem?
4. What would the sine of \(90^\circ - x\) equal in this scenario?
5. How would you find \(x\) if the triangle were not a right angle?

**Tip:** Remember that sine, cosine, and tangent functions are specific to right-angled triangles. For non-right triangles, you might need the sine or cosine rule!

Work out the value of x in the right-angled triangle with an opposite side of 3.9 cm, a hypotenuse of 4.7 cm, and an unknown angle x°.

Learn how to calculate the value of an unknown angle x in a right-angled triangle, given the opposite side (3.9 cm) and the hypotenuse (4.7 cm). This step-by-step solution uses the sine function and inverse sine to find the angle, suitable for students in Grades 8-10.

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