Question

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=3.4 kilometers and b=1.8 kilometers, what is c? If necessary, round to the nearest tenth.

Answer 1

To find the length of the hypotenuse \( c \) in a right triangle with legs \( a \) and \( b \), you can use the Pythagorean theorem, which states:

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

Given:
- \( a = 3.4 \) kilometers
- \( b = 1.8 \) kilometers

First, we need to calculate \( a^2 \) and \( b^2 \):

\[
a^2 = (3.4)^2 = 11.56
\]
\[
b^2 = (1.8)^2 = 3.24
\]

Now, add these two values:

\[
c^2 = a^2 + b^2 = 11.56 + 3.24 = 14.8
\]

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

\[
c = \sqrt{14.8} \approx 3.844
\]

Finally, round to the nearest tenth:

\[
c \approx 3.8 \text{ kilometers}
\]

Therefore, the length of the hypotenuse \( c \) is approximately **3.8 kilometers**.