Question

In a right triangle, the hypotenuse is 10 units long and one leg is 6 units long. What is the length of the other leg?(1 point)
Responses

7
7

8
8

9
9

4

Answer 1

To find the length of the other leg of the right triangle, you can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, we have:

- \( c = 10 \) (hypotenuse)
- \( a = 6 \) (one leg)
- \( b \) is the other leg that we want to find.

Plugging in the values:

\[ 6^2 + b^2 = 10^2 \]

Calculating the squares:

\[ 36 + b^2 = 100 \]

Now, subtract 36 from both sides:

\[ b^2 = 100 - 36 \]
\[ b^2 = 64 \]

Now, take the square root of both sides:

\[ b = \sqrt{64} \]
\[ b = 8 \]

So, the length of the other leg is **8 units**.

The correct response is:

**8**