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To solve for the angle \( \angle XZY \) in this right triangle, we can use trigonometric ratios. Specifically, we have the lengths of the adjacent side \( XY = 6 \, \text{cm} \) and the hypotenuse \( XZ = 15 \, \text{cm} \). Since we are dealing with the angle adjacent to the given sides, we can use the cosine function:

\[
\cos(\angle XZY) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{XY}{XZ} = \frac{6}{15}
\]

Now, we can calculate the angle \( \theta = \angle XZY \) by taking the inverse cosine (arccos) of the ratio:

\[
\theta = \cos^{-1}\left(\frac{6}{15}\right)
\]

Let me compute the value.The size of angle \( \angle XZY \) is approximately \( 66.4^\circ \), rounded to one decimal place.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would you find the size of angle \( \angle XYZ \)?
2. What trigonometric ratio would you use if you were given the opposite side instead of the adjacent?
3. How can you verify if a triangle is a right triangle using the Pythagorean theorem?
4. What is the sine of angle \( \angle XZY \)?
5. How would you find the area of this triangle using the given dimensions?

**Tip:** In a right triangle, knowing any two sides allows you to calculate any angle using basic trigonometric ratios.

Find the size of angle XZY. Give your answer to 1 decimal place.

Learn how to find the size of angle XZY in a right triangle using the cosine function. Given XY = 6 cm and XZ = 15 cm, this problem provides a step-by-step solution for calculating the angle to 1 decimal place.

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