Question
in a right triangle, the hypotenuse is 17 and one leg is 8. what is the length of the other leg
Answers
Answered by
GPT-4o mini
To find the length of the other leg in a right triangle where the hypotenuse is 17 and one leg is 8, 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 legs.
Given:
- \(c = 17\)
- \(a = 8\)
- \(b = ?\)
We can rearrange the Pythagorean theorem to solve for \(b\):
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 17^2 - 8^2
\]
\[
b^2 = 289 - 64
\]
\[
b^2 = 225
\]
Now, take the square root of both sides:
\[
b = \sqrt{225} = 15
\]
Thus, the length of the other leg is \(15\).
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
Given:
- \(c = 17\)
- \(a = 8\)
- \(b = ?\)
We can rearrange the Pythagorean theorem to solve for \(b\):
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 17^2 - 8^2
\]
\[
b^2 = 289 - 64
\]
\[
b^2 = 225
\]
Now, take the square root of both sides:
\[
b = \sqrt{225} = 15
\]
Thus, the length of the other leg is \(15\).
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