The image you provided shows two right triangles, and the task is to find the values of $x$ and $y$ for each triangle.

Triangle 1 (Problem 11):

This is a right triangle with one angle marked as $45^\circ$ and the hypotenuse labeled as 10. The variables $x$ and $y$ represent the other two sides of the triangle.

Given that it's a right triangle with a $45^\circ$ angle, it must be an isosceles right triangle (a 45-45-90 triangle). In such a triangle, the two legs are equal in length, and each leg is $\frac{1}{\sqrt{2}}$ times the length of the hypotenuse.

To find the value of $x$ and $y$, we use the following relation for a 45-45-90 triangle:

$x = y = \frac{\text{hypotenuse}}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 10 \times \frac{\sqrt{2}}{2} = 5\sqrt{2} \approx 7.07$

Thus: $x = y = 5\sqrt{2} \approx 7.07$

Triangle 2 (Problem 12):

This is another right triangle with one angle marked as $30^\circ$ and the hypotenuse labeled as $x$. The opposite side to the $30^\circ$ angle is labeled $y$, and the adjacent side is labeled $x$.

In a 30-60-90 triangle, the ratio of the sides is:

• The side opposite the $30^\circ$ angle is half the length of the hypotenuse.
• The side opposite the $60^\circ$ angle is $\frac{\sqrt{3}}{2}$ times the hypotenuse.

Since the hypotenuse is given as $x$, we can express $y$ and the other side (adjacent to the $30^\circ$ angle) in terms of $x$.

1. The side opposite the $30^\circ$ angle is: $y = \frac{1}{2}x$

2. The side adjacent to the $30^\circ$ angle (which is opposite the $60^\circ$ angle) is: $\text{Adjacent side} = \frac{\sqrt{3}}{2}x$

To fully solve for $x$ and $y$, more information is needed (either the lengths of sides or angles) to establish the exact relationship. If the side opposite the 30° angle is known, we could solve for $x$ and $y$.

Would you like more details on how to solve these problems, or do you need further clarification?