In the image, we have a right triangle $\triangle NLM$ with:

• $\overline{NL} = 15$ (the side opposite the right angle),
• $\overline{NM} = 21$ (the base or adjacent side to the right angle),
• $\overline{LM}$ (the hypotenuse) is what needs to be found.

We can use the Pythagorean theorem to solve for the hypotenuse $LM$. The Pythagorean theorem states:

$LM^2 = NL^2 + NM^2$

Substitute the given values:

$LM^2 = 15^2 + 21^2$ $LM^2 = 225 + 441$ $LM^2 = 666$

Now, take the square root of both sides to solve for $LM$:

$LM = \sqrt{666} \approx 25.8$

Thus, the length of $LM$, rounded to the nearest tenth, is approximately 25.8.

Would you like further explanation or have any questions?

Here are 5 related questions:

1. How can the Pythagorean theorem be applied to different triangles?
2. What happens if you know the hypotenuse and one side—how do you find the other side?
3. How is trigonometry used to find unknown angles in a right triangle?
4. Can the Pythagorean theorem be used for non-right triangles?
5. What are some real-world applications of the Pythagorean theorem?

Tip: In right triangles, you can use trigonometric functions like sine, cosine, or tangent if an angle and one side are known.