Example 1: Triangle $$ A B C $$ - Given: - Hypotenuse $$ A B=10 \mathrm{~cm} $$. - One leg $$ A C=6 \mathrm{~cm} $$. - $$

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To solve the problem involving triangle $$ ABC $$, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse ($$ c $$) is equal to the sum of the squares of the lengths of the other two sides ($$ a $$ and $$ b $$). The formula is given by:

$$
c^2 = a^2 + b^2
$$

In this case:
- The hypotenuse $$ AB = 10 \, \text{cm} $$ (denote this as $$ c $$).
- One leg $$ AC = 6 \, \text{cm} $$ (denote this as $$ a $$).
- We need to find the length of the other leg $$ BC $$ (denote this as $$ b $$).

### Step 1: Set up the equation

Using the Pythagorean theorem:

$$
AB^2 = AC^2 + BC^2
$$

Substituting the known values:

$$
10^2 = 6^2 + b^2
$$

### Step 2: Calculate the squares

Calculating the squares:

$$
100 = 36 + b^2
$$

### Step 3: Solve for $$ b^2 $$

Rearranging the equation to isolate $$ b^2 $$:

$$
b^2 = 100 - 36
$$

Calculating the right side:

$$
b^2 = 64
$$

### Step 4: Find $$ b $$

Taking the square root of both sides to find $$ b $$:

$$
b = \sqrt{64}
$$

Calculating the square root:

$$
b = 8 \, \text{cm}
$$

### Conclusion

The length of the other leg $$ BC $$ is $$ 8 \, \text{cm} $$.

Thus, the final answer is:
- $$ BC = 8 \, \text{cm} $$
The length of leg $$ BC $$ is $$ 8 \, \text{cm} $$.

Example 1: Triangle

Given:

Hypotenuse .

One leg .

…

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Solución

Step 1: Set up the equation

Step 2: Calculate the squares

Step 3: Solve for

Step 4: Find

Conclusion

Beyond the Answer

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