Question

what is the length of the missing leg if necessary round to the nearest tenth 6 cm 5 cm and b at the bottom is missing

Answer 1

To find the length of the missing leg \( b \) in a right triangle with legs measuring 6 cm and 5 cm, we can use the Pythagorean theorem, which states:

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

Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Since you have provided two legs and are looking for the missing leg \( b \), we will assume either \( 6 \) cm or \( 5 \) cm is a leg and you want to find the missing side using the other as a reference.

Assuming \( a = 6 \) cm and \( b = 5 \) cm:

1. **If you want to find the hypotenuse \( c \)**:
\[
c^2 = 6^2 + 5^2 = 36 + 25 = 61
\]
\[
c = \sqrt{61} \approx 7.81 \text{ cm}
\]

2. **If you want to find the length of the missing leg \( b \)** using \( c \) as the hypotenuse, you would rearrange the equation:
- Let's consider \( c \) is known and is, for instance, \( 7 \) cm:
\[
6^2 + b^2 = c^2
\]
\[
36 + b^2 = 7^2
\]
\[
36 + b^2 = 49
\]
\[
b^2 = 49 - 36
\]
\[
b^2 = 13
\]
\[
b \approx \sqrt{13} \approx 3.6 \text{ cm}
\]

Please clarify whether you want to find the hypotenuse or the other leg, and specify if additional information is available (e.g., if there is another leg or the hypotenuse).