Question

What is the length of the unknown leg in the right triangle?
A right triangle has a side with length 8 feet, hypotenuse with length StartRoot 73 EndRoot feet, and side labeled a.
3 ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft
9 ft

Answer 1

To find the length of the unknown leg \( a \) in 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 \( b \) is the length of the known leg.

Here:
- \( c = \sqrt{73} \)
- \( b = 8 \)
- \( a \) is the unknown leg.

First, we can express the Pythagorean theorem in terms of our values:

\[
a^2 + 8^2 = (\sqrt{73})^2
\]

Calculating \( 8^2 \) and \( (\sqrt{73})^2 \):

\[
a^2 + 64 = 73
\]

Now, we can solve for \( a^2 \):

\[
a^2 = 73 - 64
\]

\[
a^2 = 9
\]

Now, taking the square root of both sides:

\[
a = \sqrt{9} = 3
\]

Therefore, the length of the unknown leg \( a \) is 3 feet.

The correct answer is **3 ft**.