Question
A right triangle has a leg measuring 65 km another leg measuring 72 km what is the length of the missing leg? If necessary, round to the nearest tenth.
Answers
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the missing leg. The theorem states:
\[
c^2 = a^2 + b^2
\]
Where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, you have:
- One leg \( a = 65 \) km
- The other leg \( b = 72 \) km
To find the length of the hypotenuse \( c \), you can plug in the values:
\[
c^2 = 65^2 + 72^2
\]
Calculating \( 65^2 \):
\[
65^2 = 4225
\]
Calculating \( 72^2 \):
\[
72^2 = 5184
\]
Now, add these two results:
\[
c^2 = 4225 + 5184 = 9409
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{9409}
\]
Calculating the square root:
\[
c \approx 97.0 \text{ km}
\]
Therefore, the length of the hypotenuse is approximately **97.0 km**.
\[
c^2 = a^2 + b^2
\]
Where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, you have:
- One leg \( a = 65 \) km
- The other leg \( b = 72 \) km
To find the length of the hypotenuse \( c \), you can plug in the values:
\[
c^2 = 65^2 + 72^2
\]
Calculating \( 65^2 \):
\[
65^2 = 4225
\]
Calculating \( 72^2 \):
\[
72^2 = 5184
\]
Now, add these two results:
\[
c^2 = 4225 + 5184 = 9409
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{9409}
\]
Calculating the square root:
\[
c \approx 97.0 \text{ km}
\]
Therefore, the length of the hypotenuse is approximately **97.0 km**.