Question
What is the length of the missing leg? One of the legs are 65 cm and the height is 39 cm. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle where one leg is 65 cm and the height (the other leg) is 39 cm, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.
In your case, we have:
- One leg (\(a\)) = 65 cm
- The height (\(b\)) = 39 cm
To find the hypotenuse \(c\):
\[
c^2 = a^2 + b^2
\]
Calculating \(a^2\) and \(b^2\):
\[
65^2 = 4225
\]
\[
39^2 = 1521
\]
Now, add \(a^2\) and \(b^2\):
\[
c^2 = 4225 + 1521 = 5746
\]
Next, we find \(c\) by taking the square root of 5746:
\[
c = \sqrt{5746} \approx 75.8 \, \text{cm}
\]
So, the hypotenuse is approximately 75.8 cm.
If you need the length of the missing leg depending on different interpretations (e.g., height is the hypotenuse), please clarify the specifics, and I can assist further!
\[
a^2 + b^2 = c^2
\]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.
In your case, we have:
- One leg (\(a\)) = 65 cm
- The height (\(b\)) = 39 cm
To find the hypotenuse \(c\):
\[
c^2 = a^2 + b^2
\]
Calculating \(a^2\) and \(b^2\):
\[
65^2 = 4225
\]
\[
39^2 = 1521
\]
Now, add \(a^2\) and \(b^2\):
\[
c^2 = 4225 + 1521 = 5746
\]
Next, we find \(c\) by taking the square root of 5746:
\[
c = \sqrt{5746} \approx 75.8 \, \text{cm}
\]
So, the hypotenuse is approximately 75.8 cm.
If you need the length of the missing leg depending on different interpretations (e.g., height is the hypotenuse), please clarify the specifics, and I can assist further!