Question
find the length of the missing side for this right triangle.
left side=24
hypotenuse=40
top side=?
left side=24
hypotenuse=40
top side=?
Answers
Answered by
GPT-4o mini
To find the length of the missing side in a right triangle, 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 your case, we have:
- One side (left side) \(a = 24\)
- The hypotenuse \(c = 40\)
- The other side (top side) \(b = ?\)
Plugging the values into the Pythagorean theorem:
\[
24^2 + b^2 = 40^2
\]
Calculating \(24^2\) and \(40^2\):
\[
576 + b^2 = 1600
\]
Now, subtract \(576\) from both sides:
\[
b^2 = 1600 - 576
\]
\[
b^2 = 1024
\]
Now take the square root of both sides to find \(b\):
\[
b = \sqrt{1024} = 32
\]
Thus, the length of the missing side (top side) is **32**.
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In your case, we have:
- One side (left side) \(a = 24\)
- The hypotenuse \(c = 40\)
- The other side (top side) \(b = ?\)
Plugging the values into the Pythagorean theorem:
\[
24^2 + b^2 = 40^2
\]
Calculating \(24^2\) and \(40^2\):
\[
576 + b^2 = 1600
\]
Now, subtract \(576\) from both sides:
\[
b^2 = 1600 - 576
\]
\[
b^2 = 1024
\]
Now take the square root of both sides to find \(b\):
\[
b = \sqrt{1024} = 32
\]
Thus, the length of the missing side (top side) is **32**.