Question

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=7 kilometers and b=6 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 \( b \), we can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

Given \( a = 7 \) kilometers and \( b = 6 \) kilometers, we can substitute these values into the formula:

\[
c = \sqrt{7^2 + 6^2}
\]

Calculating the squares of \( a \) and \( b \):

\[
7^2 = 49 \quad \text{and} \quad 6^2 = 36
\]

Adding these values together:

\[
c = \sqrt{49 + 36} = \sqrt{85}
\]

Now we need to calculate \( \sqrt{85} \).

\[
\sqrt{85} \approx 9.21954445729
\]

Rounding this to the nearest tenth:

\[
c \approx 9.2 \text{ kilometers}
\]

Thus, the length of the hypotenuse \( c \) is approximately \( \boxed{9.2} \) kilometers.