https://file.aiquickdraw.com/mathbot/file/1729516646394qpbglz2n.jpg

This is a right-angled triangle with side lengths given as 15.6 cm and 13.8 cm, and the hypotenuse is 24.9 cm. The problem asks to find the length of the unknown side labeled as "a", which is opposite the right angle.

We can use the **Pythagorean theorem** to solve for the unknown side, which states:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the hypotenuse (24.9 cm),
- \(a\) and \(b\) are the two other sides (one of them is 15.6 cm, and the other is 13.8 cm).

Since the hypotenuse \(c = 24.9 \, \text{cm}\), and we know the other two sides, we can check for consistency or solve using the formula:

\[
a^2 + b^2 = c^2
\]

Calculating:

\[
a^2 + 13.8^2 = 24.9^2
\]
\[
a^2 + 190.44 = 620.01
\]
\[
a^2 = 620.01 - 190.44 = 429.57
\]
\[
a = \sqrt{429.57} \approx 20.73 \, \text{cm}
\]

Thus, the length of the unknown side \(a\) is approximately **20.73 cm**.

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Would you like more details or have any further questions?

Here are five related questions:
1. What would happen if we had two different side lengths given?
2. How does the Pythagorean theorem apply to non-right triangles?
3. Can you calculate the area of this triangle?
4. How would you verify if the given sides form a valid right triangle?
5. What are some real-life applications of the Pythagorean theorem?

**Tip:** The Pythagorean theorem only works for right-angled triangles. For non-right triangles, other methods like the Law of Cosines are used.

Find the length of the unknown side in a right-angled triangle with side lengths 15.6 cm, 13.8 cm, and hypotenuse 24.9 cm.

Solve a right-angled triangle problem by finding the unknown side with given lengths 15.6 cm and 13.8 cm, and the hypotenuse of 24.9 cm. Using the Pythagorean Theorem, the solution demonstrates how to calculate the length of the unknown side as approximately 20.73 cm.

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