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In this right triangle \( \triangle ABC \), we are tasked with solving for \( x \), which is the side adjacent to the 70° angle at \( C \). Given that:

- \( AB = 8 \) is the hypotenuse,
- \( \angle ACB = 70^\circ \),
- \( \angle ABC = 90^\circ \) (right angle).

We can use trigonometric functions to solve for \( x \). Since we have the hypotenuse and are looking for the adjacent side to the angle \( 70^\circ \), we will use the cosine function:

\[
\cos(70^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{8}
\]

Solving for \( x \):

\[
x = 8 \cdot \cos(70^\circ)
\]

Let me calculate that for you.The value of \( x \) is approximately \( 2.7 \) when rounded to the nearest tenth.

Would you like more details, or do you have any further questions?

Here are some related questions for further practice:
1. What is the length of the side opposite the \( 70^\circ \) angle?
2. How would the calculation change if the given angle were \( 50^\circ \) instead?
3. Can you calculate the area of triangle \( ABC \)?
4. How would you solve for \( x \) using the sine or tangent function?
5. What if the hypotenuse were a different length, say \( 10 \)? How would that affect \( x \)?

**Tip:** In right triangles, the cosine function is always used to relate the adjacent side to the hypotenuse.

Solve for x. Round to the nearest tenth, if necessary.

Learn how to solve for x in a right triangle using the cosine function. This problem involves trigonometric concepts such as adjacent, hypotenuse, and cosine of a given angle, suitable for students in Grades 9-10. Step-by-step solution included.

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