Question
Find the approximate length of the leg of a right triangle with one leg length 8 and hypotenuse length 19.
20.6
17.2
17.7
20.3
20.6
17.2
17.7
20.3
Answers
Answered by
GPT-4o mini
To find the length of the leg of the 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 two legs of the triangle. Given one leg length is 8 and the hypotenuse length is 19, we can denote:
- \( a = 8 \)
- \( c = 19 \)
- \( b \) (the unknown leg) is what we need to find.
Using the Pythagorean theorem, we can rearrange to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Now substituting the known values:
\[
b^2 = 19^2 - 8^2
\]
Calculating \( 19^2 \) and \( 8^2 \):
\[
19^2 = 361
\]
\[
8^2 = 64
\]
Now substitute these values back into the equation:
\[
b^2 = 361 - 64
\]
\[
b^2 = 297
\]
Taking the square root of both sides gives us \( b \):
\[
b = \sqrt{297} \approx 17.23
\]
The approximate value of \( b \) is about 17.2.
The correct answer is:
**17.2**
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs of the triangle. Given one leg length is 8 and the hypotenuse length is 19, we can denote:
- \( a = 8 \)
- \( c = 19 \)
- \( b \) (the unknown leg) is what we need to find.
Using the Pythagorean theorem, we can rearrange to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Now substituting the known values:
\[
b^2 = 19^2 - 8^2
\]
Calculating \( 19^2 \) and \( 8^2 \):
\[
19^2 = 361
\]
\[
8^2 = 64
\]
Now substitute these values back into the equation:
\[
b^2 = 361 - 64
\]
\[
b^2 = 297
\]
Taking the square root of both sides gives us \( b \):
\[
b = \sqrt{297} \approx 17.23
\]
The approximate value of \( b \) is about 17.2.
The correct answer is:
**17.2**