Question
What is the length of the unknown side of the right triangle?
14
7
a
(1 point)
Responses
7 ft.
7 ft.
147−−−√ ft.
147−−−√ ft.
14−−√ ft.
14−−√ ft.
21 ft.
14
7
a
(1 point)
Responses
7 ft.
7 ft.
147−−−√ ft.
147−−−√ ft.
14−−√ ft.
14−−√ ft.
21 ft.
Answers
GPT-4o mini
To find the unknown side \( a \) of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \):
\[
a^2 + b^2 = c^2
\]
In your case, you provided two sides of the triangle: one side is \( 7 \) and the hypotenuse is \( 14 \). Therefore, we can set up the equation:
\[
7^2 + a^2 = 14^2
\]
Calculating the squares:
\[
49 + a^2 = 196
\]
Now, we solve for \( a^2 \):
\[
a^2 = 196 - 49
\]
\[
a^2 = 147
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{147}
\]
Thus, the length of the unknown side \( a \) is:
\[
\sqrt{147} \text{ ft.}
\]
So the correct option is:
**147−−−√ ft.**
\[
a^2 + b^2 = c^2
\]
In your case, you provided two sides of the triangle: one side is \( 7 \) and the hypotenuse is \( 14 \). Therefore, we can set up the equation:
\[
7^2 + a^2 = 14^2
\]
Calculating the squares:
\[
49 + a^2 = 196
\]
Now, we solve for \( a^2 \):
\[
a^2 = 196 - 49
\]
\[
a^2 = 147
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{147}
\]
Thus, the length of the unknown side \( a \) is:
\[
\sqrt{147} \text{ ft.}
\]
So the correct option is:
**147−−−√ ft.**