The image shows a trigonometry question involving a triangle and a given ratio of sides PQ:QR. Based on the text, it appears you're asked to find the cosine of angle y, given the ratio of PQ to QR is 2:5.

It looks like there’s a mistake in the ratio setup in the notes written on the image, as they attempt to find unknown sides using that ratio.

To solve this problem properly, we need to use the given ratio PQ:QR = 2:5 to determine the missing side lengths. The triangle involves trigonometric properties that could include the Pythagorean theorem or the cosine rule.

Here’s a rough breakdown of how you might approach this:

1. Label the sides correctly: Use the ratio to determine the lengths of PQ and QR.
2. Apply trigonometric identities: Use the cosine rule if the angle y is involved in a non-right triangle or the cosine definition for a right triangle.

Would you like me to proceed with solving the question? I can go into more detail or clarify any part you want. Let me know if you want help with these steps.

Questions to expand:

1. How do you apply the cosine rule in a non-right triangle?
2. What is the relationship between the sides in a triangle when using trigonometric ratios?
3. Can the Pythagorean theorem be used in this problem, and when?
4. How does the sine rule relate to this problem setup?
5. What are other ways to express trigonometric ratios like cosine, sine, and tangent?

Tip: Always check if the triangle is right-angled first, as that simplifies solving trigonometric problems.