Two legs of a right triangle are 8 cm and 15 cm long. Find the length of the hypotenuse of the triangle.

Answer

To find the length of the hypotenuse of a right triangle with legs measuring 8 cm and 15 cm, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

### Step-by-Step Solution:

1. **Identify the lengths of the legs**:
- Let the lengths of the two legs be:
- \( a = 8 \, \text{cm} \)
- \( b = 15 \, \text{cm} \)

2. **Apply the Pythagorean theorem**:
- The formula is:
\[ c^2 = a^2 + b^2 \]
- Here, \( c \) is the length of the hypotenuse.

3. **Calculate the squares of the legs**:
- Calculate \( a^2 \):
\[ a^2 = 8^2 = 64 \]
- Calculate \( b^2 \):
\[ b^2 = 15^2 = 225 \]

4. **Add the squares of the legs**:
- Now add \( a^2 \) and \( b^2 \):
\[ c^2 = 64 + 225 = 289 \]

5. **Find the length of the hypotenuse**:
- To find \( c \), take the square root of \( c^2 \):
\[ c = \sqrt{289} = 17 \, \text{cm} \]

### Final Answer:
The length of the hypotenuse is \( 17 \, \text{cm} \).