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I see that you've uploaded a worksheet with five triangle problems, and each asks for the values of \(x\), \(y\), and \(z\). I'll go through each problem and help you solve them.

### Problem 1
In this triangle, we can use trigonometric ratios (sine, cosine, or tangent) because one angle is known and two sides are given.

- Given:
  - Angle \( \theta = 20^\circ \)
  - Opposite side = 10
  - Adjacent side = \( z \)

We can use tangent here:
\[
\tan(20^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{10}{z}
\]
From this, we can solve for \(z\). Similarly, using sine or cosine, we can find \(x\) and \(y\).

### Problem 2
This appears to be a right triangle, where:
- \(y\) is opposite to the right angle.
- One side is \(x\), and the other side is 6.
- The hypotenuse \(z\) can be found using the Pythagorean theorem:
\[
x^2 + 6^2 = z^2
\]

### Problem 3
This triangle also involves trigonometric identities, as one angle is \(65^\circ\), and two sides are given. We will proceed similarly by applying the tangent or cosine rule.

### Problem 4
In this triangle:
- We have \(x\), \(y\), and \(z\) all labeled, and we will use the given values to solve using appropriate rules of trigonometry.

Would you like me to continue solving each step?

Find the values of x, y, and z for a series of triangles using trigonometric rules and theorems.

Learn how to solve right triangle problems and find values of x, y, and z using trigonometric ratios like sine, cosine, and tangent. Apply the Pythagorean theorem for accurate results, suitable for Grades 8-10 students.

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