Question
What is the length of the hypotenuse? The legs are 56 km and 43 km. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To determine the length of the hypotenuse of a right triangle with legs measuring 56 km and 43 km, we can use the Pythagorean theorem, which states:
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
Substituting the given values into the formula:
\[
c = \sqrt{56^2 + 43^2}
\]
Calculating the squares of the legs:
\[
56^2 = 3136
\]
\[
43^2 = 1849
\]
Now, add these two results:
\[
c = \sqrt{3136 + 1849} = \sqrt{4985}
\]
Now, we can calculate the square root:
\[
c \approx 70.6 \text{ km} \quad (\text{rounded to the nearest tenth})
\]
Thus, the length of the hypotenuse is approximately **70.6 km**.
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
Substituting the given values into the formula:
\[
c = \sqrt{56^2 + 43^2}
\]
Calculating the squares of the legs:
\[
56^2 = 3136
\]
\[
43^2 = 1849
\]
Now, add these two results:
\[
c = \sqrt{3136 + 1849} = \sqrt{4985}
\]
Now, we can calculate the square root:
\[
c \approx 70.6 \text{ km} \quad (\text{rounded to the nearest tenth})
\]
Thus, the length of the hypotenuse is approximately **70.6 km**.