Asked by dee
What is the length of the unknown side of the right triangle?(1 point)Responses3 ft.3 ft.9 ft.9 ft.57−−√ ft.57−−√ ft.65−−√ ft.
Answers
Answered by
dee
8ft 73ft
Answered by
GPT-4o mini
To find the length of the unknown side of a right triangle, we typically 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.
However, in order to provide a specific answer, I would need to know the lengths of at least one side (either \(a\) or \(b\)) and the length of the hypotenuse \(c\).
Could you provide additional information about the lengths of the known sides or clarify your question further?
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
However, in order to provide a specific answer, I would need to know the lengths of at least one side (either \(a\) or \(b\)) and the length of the hypotenuse \(c\).
Could you provide additional information about the lengths of the known sides or clarify your question further?
Answered by
GPT-4o mini
It seems like you provided the lengths of two sides of a right triangle: 8 ft and 73 ft. We need to determine which side (if either) is the hypotenuse.
1. **Assuming 73 ft is the hypotenuse** and 8 ft is one of the other sides, we can use the Pythagorean theorem to find the unknown side \(b\):
\[
a^2 + b^2 = c^2
\]
Substituting the known values:
\[
8^2 + b^2 = 73^2
\]
Calculating the squares:
\[
64 + b^2 = 5329
\]
Now, subtract 64 from both sides:
\[
b^2 = 5329 - 64
\]
\[
b^2 = 5265
\]
Taking the square root:
\[
b = \sqrt{5265} \approx 72.6 \text{ ft}
\]
2. **Assuming 8 ft is the hypotenuse** and 73 ft is one of the sides would not be possible, as the hypotenuse must be the longest side.
Thus, if 73 ft is the hypotenuse, the unknown side (the other leg of the triangle) is approximately **72.6 ft**. If you have additional details or a specific number from your choices, please let me know!
1. **Assuming 73 ft is the hypotenuse** and 8 ft is one of the other sides, we can use the Pythagorean theorem to find the unknown side \(b\):
\[
a^2 + b^2 = c^2
\]
Substituting the known values:
\[
8^2 + b^2 = 73^2
\]
Calculating the squares:
\[
64 + b^2 = 5329
\]
Now, subtract 64 from both sides:
\[
b^2 = 5329 - 64
\]
\[
b^2 = 5265
\]
Taking the square root:
\[
b = \sqrt{5265} \approx 72.6 \text{ ft}
\]
2. **Assuming 8 ft is the hypotenuse** and 73 ft is one of the sides would not be possible, as the hypotenuse must be the longest side.
Thus, if 73 ft is the hypotenuse, the unknown side (the other leg of the triangle) is approximately **72.6 ft**. If you have additional details or a specific number from your choices, please let me know!