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The triangle shown is a right triangle with one of its angles being 60°, the hypotenuse is 16, and we are asked to find the value of \( x \), which is the length of the side adjacent to the 60° angle.

To solve this, we can use trigonometric ratios. Specifically, we use the cosine function because we have the adjacent side (\( x \)) and the hypotenuse (16).

The cosine of an angle in a right triangle is given by:

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

For \( \theta = 60^\circ \):

\[
\cos(60^\circ) = \frac{x}{16}
\]

We know that \( \cos(60^\circ) = \frac{1}{2} \), so:

\[
\frac{1}{2} = \frac{x}{16}
\]

Now, solve for \( x \):

\[
x = 16 \times \frac{1}{2} = 8
\]

Thus, the value of \( x \) is 8. The correct answer is option **B**.

Would you like more details or have any questions about this solution?

Here are 5 related questions you can consider:
1. How would the solution change if the given angle were 30° instead of 60°?
2. What trigonometric function would be used to find the opposite side of the triangle?
3. How can you apply the Pythagorean theorem to verify the answer?
4. What are the exact trigonometric values of sine and cosine for common angles (30°, 45°, 60°)?
5. How would the problem differ if the given side were the adjacent and the opposite side was unknown?

**Tip:** When dealing with right triangles, using trigonometric ratios like sine, cosine, and tangent is very effective for solving for unknown sides.

In the triangle shown, what is the value of x?

Learn how to solve for the adjacent side in a right triangle using the cosine function with a 60° angle and a hypotenuse of 16. This problem is suitable for students in Grades 9-10 and covers trigonometric ratios and right triangle principles.

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