Question
What is the length of the unknown side of the right triangle?
8ft
73ft
a
(1 point)
Responses
3 ft.
3 ft.
65−−√ ft.
65−−√ ft.
57−−√ ft.
57−−√ ft.
9 ft.
8ft
73ft
a
(1 point)
Responses
3 ft.
3 ft.
65−−√ ft.
65−−√ ft.
57−−√ ft.
57−−√ ft.
9 ft.
Answers
GPT-4o mini
To find the length of the unknown side of 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 of 8 ft (we can let this be \( a \)), one side of 73 ft (which will be the hypotenuse \( c \)), and the unknown side (let's call it \( b \)).
Using the Pythagorean theorem:
\[
8^2 + b^2 = 73^2
\]
Calculating the squares:
\[
64 + b^2 = 5329
\]
Now, isolating \( b^2 \):
\[
b^2 = 5329 - 64
\]
\[
b^2 = 5265
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{5265}
\]
This doesn't exactly match the options you provided. Let's approximate \( \sqrt{5265} \):
Calculating \( \sqrt{5265} \) gives approximately 72.5 ft, which is not one of the given options.
Given the lengths provided in your options, it seems there might be a misinterpretation in the triangle's dimensions or the specific numbers you've shared.
Please double-check the side lengths or provide any additional context to help find the correct answer.
\[ a^2 + b^2 = c^2 \]
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 of 8 ft (we can let this be \( a \)), one side of 73 ft (which will be the hypotenuse \( c \)), and the unknown side (let's call it \( b \)).
Using the Pythagorean theorem:
\[
8^2 + b^2 = 73^2
\]
Calculating the squares:
\[
64 + b^2 = 5329
\]
Now, isolating \( b^2 \):
\[
b^2 = 5329 - 64
\]
\[
b^2 = 5265
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{5265}
\]
This doesn't exactly match the options you provided. Let's approximate \( \sqrt{5265} \):
Calculating \( \sqrt{5265} \) gives approximately 72.5 ft, which is not one of the given options.
Given the lengths provided in your options, it seems there might be a misinterpretation in the triangle's dimensions or the specific numbers you've shared.
Please double-check the side lengths or provide any additional context to help find the correct answer.