The image shows a right triangle with a 45° angle and a 60° angle, implying it is a special 45°-45°-90° triangle. The question asks to find the values of $x$ and $y$ for this triangle. In a 45°-45°-90° triangle, the legs are equal, and the relationship between the legs $x$ and the hypotenuse $y$ follows:

$y = x \times \sqrt{2}$

Given that the hypotenuse $y = 60$, we can solve for $x$:

$x = \frac{y}{\sqrt{2}} = \frac{60}{\sqrt{2}} \approx 42.43$

The values should correspond to:

• $x \approx 42.43$ units
• $y = 60$ units

However, none of the provided answers match exactly due to rounding or possible error, but the best match might be found in another setup or closer inspection.

Would you like more details or have further questions about this calculation?

Here are five related questions to deepen your understanding:

1. How do the side lengths of a 45°-45°-90° triangle relate to each other?
2. Why is the hypotenuse always longer than the legs in this type of triangle?
3. How would you calculate the side lengths if the hypotenuse is a decimal value?
4. What is the significance of the Pythagorean theorem in this problem?
5. How can you use trigonometric functions to solve for side lengths in right triangles?

Tip: In a 45°-45°-90° triangle, the ratio between the legs and the hypotenuse is always 1:1:$\sqrt{2}$.