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 Bepaal telkens de lengte van het gevraagde lijnstuk.


To solve the problem of determining the length of the unknown line segment \( KL \) (denoted as \( ? \) in the triangle), we can use the Pythagorean Theorem.

### Step 1: Identify the right triangles
In the given diagram, \( \triangle KLM \) and \( \triangle KNM \) are right triangles, and since \( L \) is the right angle in \( \triangle KLM \), we can focus on using the Pythagorean theorem here.

### Step 2: Apply the Pythagorean Theorem
For \( \triangle KLM \):

\[
KM^2 = KL^2 + LM^2
\]

We are given \( KM = 10 \) and \( LM = 3 \). We need to find \( KL \).

### Step 3: Substitute the known values

\[
10^2 = KL^2 + 3^2
\]

\[
100 = KL^2 + 9
\]

### Step 4: Solve for \( KL \)

\[
KL^2 = 100 - 9 = 91
\]

\[
KL = \sqrt{91} \approx 9.54
\]

So, the length of \( KL \) is approximately 9.54 units.

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Would you like more details, or do you have any further questions?

Here are some related questions you might consider:

1. What is the exact value of \( \sqrt{91} \)?
2. Can you determine the length of \( KN \) using similar triangles?
3. How would the calculation change if \( LM \) were different?
4. Can you verify \( \triangle KLM \) using trigonometric identities?
5. How would you calculate the area of \( \triangle KLM \)?

**Tip:** When dealing with right triangles, always check if the Pythagorean theorem is applicable to simplify your calculations.

Learn how to determine the length of the unknown line segment KL in a right triangle using the Pythagorean Theorem. Detailed step-by-step solution provided with calculations. Suitable for Grades 9-12 students studying geometry and right triangles.

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