Question
What is the length of the missing side of the triangle below? If needed, please round to the nearest tenth.
The longer leg is length 7
the shorter leg is length 5
the hypotenuse is missing
The longer leg is length 7
the shorter leg is length 5
the hypotenuse is missing
Answers
GPT-4o mini
To find the length of the hypotenuse of a right triangle where you know the lengths of the two legs, you can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case, the longer leg \( a \) is 7, and the shorter leg \( b \) is 5. Plugging in these values gives:
\[
c^2 = 7^2 + 5^2
\]
\[
c^2 = 49 + 25
\]
\[
c^2 = 74
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{74} \approx 8.6
\]
Thus, the length of the hypotenuse, rounded to the nearest tenth, is approximately **8.6**.
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case, the longer leg \( a \) is 7, and the shorter leg \( b \) is 5. Plugging in these values gives:
\[
c^2 = 7^2 + 5^2
\]
\[
c^2 = 49 + 25
\]
\[
c^2 = 74
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{74} \approx 8.6
\]
Thus, the length of the hypotenuse, rounded to the nearest tenth, is approximately **8.6**.