Okay, I will help you solve the problem. Based on the image, it looks like we need to find the values of w and y in the right triangle.

Task 18

We are given a right triangle with one angle of 60 degrees and the hypotenuse equal to 10. We need to find the length of the side w, which is opposite to the 60-degree angle.

We can use the sine function to relate the angle, the opposite side, and the hypotenuse:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

In this case, $\theta = 60^\circ$, the opposite side is w, and the hypotenuse is 10. So we have:

$\sin(60^\circ) = \frac{w}{10}$

We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$. Therefore:

$\frac{\sqrt{3}}{2} = \frac{w}{10}$

To solve for w, we multiply both sides by 10:

$w = 10 \cdot \frac{\sqrt{3}}{2} = 5\sqrt{3}$

So, $w = 5\sqrt{3}$.

Answer: $w = 5\sqrt{3}$

Task 19

Now we need to find the length of the side y, which is adjacent to the 60-degree angle.

We can use the cosine function to relate the angle, the adjacent side, and the hypotenuse:

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

In this case, $\theta = 60^\circ$, the adjacent side is y, and the hypotenuse is 10. So we have:

$\cos(60^\circ) = \frac{y}{10}$

We know that $\cos(60^\circ) = \frac{1}{2}$. Therefore:

$\frac{1}{2} = \frac{y}{10}$

To solve for y, we multiply both sides by 10:

$y = 10 \cdot \frac{1}{2} = 5$

So, $y = 5$.

Answer: $y = 5$

Okay, I see that you're asking about the value of y in the given right triangle.

Task 19

As I calculated before, the length of the side y, which is adjacent to the 60-degree angle, is found using the cosine function:

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

In this case, $\theta = 60^\circ$, the adjacent side is y, and the hypotenuse is 10. So we have:

$\cos(60^\circ) = \frac{y}{10}$

Since $\cos(60^\circ) = \frac{1}{2}$, we have:

$\frac{1}{2} = \frac{y}{10}$

To solve for y, we multiply both sides by 10:

$y = 10 \cdot \frac{1}{2} = 5$

So, $y = 5$.

Answer: $y = 5$