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 Bepaal telkens de lengte van het gevraagde lijnstuk.


To determine the length of the missing line segment \( SR \) in the triangle, we can analyze the information given in the diagram. Let's review what we know:

1. Triangle \( PRQ \) has a known side length:
   - \( PR = 5 \)
   - \( RQ = 13 \)

2. We need to find the length of line segment \( SR \).

Since \( PRQ \) appears to be a right triangle with \( PQ \) as the hypotenuse, we can apply the Pythagorean theorem to find the length of \( PQ \).

### Step-by-step Solution:

1. **Apply the Pythagorean Theorem**:

\[
PQ^2 = PR^2 + RQ^2
\]

\[
PQ^2 = 5^2 + 13^2
\]

\[
PQ^2 = 25 + 169 = 194
\]

\[
PQ = \sqrt{194}
\]

2. **Use the Law of Cosines in Triangle \( PRS \) to find \( SR \)**:

We can use the Law of Cosines if we knew the angles, but if \( \triangle PRS \) is also a right triangle, then we might not need it. However, we do not have any angles mentioned. If \( PR \) and \( QR \) are perpendicular, and if \( PRS \) forms another triangle, we might assume a specific configuration or check if it’s a similarity ratio.

Instead, **given information** usually leads directly to use of either Pythagoras in \( \triangle SQR \) or right triangle identification and recognizing if similar or parallel alignments.

For now, without angles or complete information, we hold our answer.

3. **Alternate Analysis or Further Clarity to Update**

Would you like to delve deeper into a specific line of understanding or any details possibly about \( S \), \( R \)?

Learn how to determine the length of line segment SR in triangle PRQ using the Pythagorean theorem and the Law of Cosines. This problem involves analyzing known side lengths of a triangle and applying geometric theorems to find the missing side length. Suitable for high school students studying geometry and trigonometry.

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