Question

5 km left side
a = right side
2 km bottom
What is the length of the missing leg? If necessary, round to the nearest tenth.
a=
kilometers

Answer 1

To find the length of the missing leg when given the lengths of the other two legs in a right triangle, you can use the Pythagorean theorem:

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

Where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two legs.

In your case:
- One leg is 5 km (let's consider this as \( a \)),
- The other leg is 2 km (let's consider this as \( b \)).

We want to find the hypotenuse \( c \).

Using the Pythagorean theorem:

\[
c^2 = 5^2 + 2^2
\]

Calculating each term:

\[
c^2 = 25 + 4
\]
\[
c^2 = 29
\]

Now, take the square root of both sides to find \( c \):

\[
c = \sqrt{29} \approx 5.385
\]

Rounding to the nearest tenth:

\[
c \approx 5.4 \text{ km}
\]

Thus, the length of the hypotenuse (missing leg) is approximately **5.4 kilometers**.