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What is the approximate value of *x*? Round to the nearest tenth.

The triangle in the image is a right-angled triangle, with one angle measuring \(50^\circ\) and the opposite side (adjacent to the right angle) labeled as 6 cm. We need to calculate the length of side \(x\), which is the side adjacent to the \(50^\circ\) angle.

We can use trigonometric ratios to solve this. Specifically, the cosine function relates the adjacent side to the hypotenuse:

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

In this case:

\[
\cos(50^\circ) = \frac{6}{x}
\]

To solve for \(x\), rearrange the equation:

\[
x = \frac{6}{\cos(50^\circ)}
\]

Now, calculating \(x\):

\[
x = \frac{6}{\cos(50^\circ)} \approx \frac{6}{0.6428} \approx 9.3 \, \text{cm}
\]

So, the approximate value of \(x\) is **9.3 cm**.

Would you like further details or explanations?

Here are some related questions you might consider:
1. How do we find side \(y\) using trigonometric ratios?
2. What is the sine rule, and could it apply here?
3. Can the Pythagorean theorem be used once we know two sides?
4. How do we calculate the area of this triangle?
5. What is the perimeter of the triangle once all sides are known?

**Tip**: When working with right triangles, identify which trigonometric ratio (sine, cosine, or tangent) best fits the known information to simplify calculations.

What is the approximate value of x? Round to the nearest tenth.

Learn how to calculate the hypotenuse of a right-angled triangle with a 50-degree angle and a 6 cm adjacent side. The solution involves using trigonometric ratios and the cosine formula to find the length of the hypotenuse, rounding to the nearest tenth. This problem is suitable for students in Grades 9-11.

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