Question
How do I use the Pythagorean theorem to find the length of the other leg of a right triangle when one leg is 6 cm and the hypotenuse is 10 cm?
Answers
GPT-4o mini
To find the length of the other leg of a right triangle using the Pythagorean theorem, you can follow these steps:
1. **Understand the Pythagorean theorem**: The theorem 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 legs \( a \) and \( b \). The formula is:
\[
c^2 = a^2 + b^2
\]
2. **Identify your values**: In your case:
- One leg \( a = 6 \) cm
- Hypotenuse \( c = 10 \) cm
- You need to find the length of the other leg \( b \).
3. **Plug the known values into the equation**:
\[
10^2 = 6^2 + b^2
\]
4. **Calculate the squares**:
\[
100 = 36 + b^2
\]
5. **Rearrange the equation to solve for \( b^2 \)**:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
6. **Take the square root of \( b^2 \) to find \( b \)**:
\[
b = \sqrt{64}
\]
\[
b = 8 \text{ cm}
\]
Therefore, the length of the other leg is **8 cm**.
1. **Understand the Pythagorean theorem**: The theorem 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 legs \( a \) and \( b \). The formula is:
\[
c^2 = a^2 + b^2
\]
2. **Identify your values**: In your case:
- One leg \( a = 6 \) cm
- Hypotenuse \( c = 10 \) cm
- You need to find the length of the other leg \( b \).
3. **Plug the known values into the equation**:
\[
10^2 = 6^2 + b^2
\]
4. **Calculate the squares**:
\[
100 = 36 + b^2
\]
5. **Rearrange the equation to solve for \( b^2 \)**:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
6. **Take the square root of \( b^2 \) to find \( b \)**:
\[
b = \sqrt{64}
\]
\[
b = 8 \text{ cm}
\]
Therefore, the length of the other leg is **8 cm**.