Asked by liquidlew
What is the length of the missing leg? If necessary, round to the nearest tenth.
b
=
inches
a = 17, c = 15
b
=
inches
a = 17, c = 15
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the length of the missing leg \( b \) in a right triangle, you can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
In this case, you are provided with:
- \( a = 17 \) (one leg of the triangle)
- \( c = 15 \) (the hypotenuse)
However, it seems there is a mistake in the values provided because, in any right triangle, the hypotenuse \( c \) must be the longest side. Since \( a \) is 17 and \( c \) is 15, it's not possible for \( c \) to be less than \( a \).
Please double-check the values of \( a \) and \( c \). If \( c \) is actually supposed to be more than 17, we can properly solve for \( b \) using the Pythagorean theorem.
Assuming you meant to have \( c = 17 \) and \( a = 15 \):
1. Substitute the values into the formula:
\[
15^2 + b^2 = 17^2
\]
2. Calculate:
\[
225 + b^2 = 289
\]
3. Rearranging the equation gives:
\[
b^2 = 289 - 225
\]
\[
b^2 = 64
\]
4. Take the square root of both sides:
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Thus, the length of the missing leg \( b \) is \( 8 \) inches.
If this isn't accurate due to a misunderstanding of the triangle's side lengths, please clarify.
\[
a^2 + b^2 = c^2
\]
In this case, you are provided with:
- \( a = 17 \) (one leg of the triangle)
- \( c = 15 \) (the hypotenuse)
However, it seems there is a mistake in the values provided because, in any right triangle, the hypotenuse \( c \) must be the longest side. Since \( a \) is 17 and \( c \) is 15, it's not possible for \( c \) to be less than \( a \).
Please double-check the values of \( a \) and \( c \). If \( c \) is actually supposed to be more than 17, we can properly solve for \( b \) using the Pythagorean theorem.
Assuming you meant to have \( c = 17 \) and \( a = 15 \):
1. Substitute the values into the formula:
\[
15^2 + b^2 = 17^2
\]
2. Calculate:
\[
225 + b^2 = 289
\]
3. Rearranging the equation gives:
\[
b^2 = 289 - 225
\]
\[
b^2 = 64
\]
4. Take the square root of both sides:
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Thus, the length of the missing leg \( b \) is \( 8 \) inches.
If this isn't accurate due to a misunderstanding of the triangle's side lengths, please clarify.
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