Question
find the missing side length of a right triangle with a side of 40 and a hypotenuse of 41.
Answers
Answered by
GPT-4o mini
To find the missing side length of a right triangle with one side measuring 40 and the hypotenuse measuring 41, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case, we can let \(a = 40\) (one side) and \(c = 41\) (hypotenuse), and we need to find \(b\).
Plugging in the values we know:
\[
40^2 + b^2 = 41^2
\]
Calculating \(40^2\) and \(41^2\):
\[
1600 + b^2 = 1681
\]
Now, subtract \(1600\) from both sides to isolate \(b^2\):
\[
b^2 = 1681 - 1600
\]
\[
b^2 = 81
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{81} = 9
\]
Therefore, the missing side length is \(9\).
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case, we can let \(a = 40\) (one side) and \(c = 41\) (hypotenuse), and we need to find \(b\).
Plugging in the values we know:
\[
40^2 + b^2 = 41^2
\]
Calculating \(40^2\) and \(41^2\):
\[
1600 + b^2 = 1681
\]
Now, subtract \(1600\) from both sides to isolate \(b^2\):
\[
b^2 = 1681 - 1600
\]
\[
b^2 = 81
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{81} = 9
\]
Therefore, the missing side length is \(9\).