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The problem involves a right-angled triangle, where one angle is \( 28^\circ \), the adjacent side to the angle is 4 cm, and the hypotenuse is labeled as \( x \). To find the hypotenuse, we can use trigonometry, specifically the cosine function, which relates the adjacent side and hypotenuse in a right triangle.

The cosine formula is:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Substituting the given values:

\[
\cos(28^\circ) = \frac{4}{x}
\]

Now solve for \( x \):

\[
x = \frac{4}{\cos(28^\circ)}
\]

Let me calculate the value of \( x \).The length of the missing side \( x \) is approximately \( 4.5 \) cm, rounded to 1 decimal place.

Do you have any questions or need further details?

Here are five related questions to expand on this:

1. How would you use the sine function to solve for other sides of the triangle?
2. Can you solve for the missing side if the opposite side was given instead of the adjacent?
3. What happens to the value of \( x \) if the angle increases?
4. How can you verify the answer using the Pythagorean theorem?
5. How would the result change if the angle was \( 90^\circ - 28^\circ \)?

**Tip**: Always ensure your calculator is in degree mode when working with angles in degrees.

Find the length of the missing side x in a right-angled triangle, where the angle is 28° and the adjacent side is 4 cm.

Learn how to calculate the missing hypotenuse in a right-angled triangle using the cosine function, where the angle is 28° and the adjacent side is 4 cm. This trigonometry problem demonstrates the use of basic trig functions and is suitable for students in Grades 9-11.

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