Question

What is the length of the unknown side of the right triangle?
8 ft, √73 ft, a


(1 point)
Responses

9 ft.
9 ft.

3 ft.
3 ft.

65−−√ ft.
65−−√ ft.

57−−√ ft.

Answer 1

To find the length of the unknown side \( a \) in 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 (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.

Assuming \( 8 \, \text{ft} \) and \( \sqrt{73} \, \text{ft} \) are the lengths of the two legs, we will determine which is the hypotenuse. The hypotenuse must be the longer side.

1. Calculate \( 8^2 \):
\[
8^2 = 64
\]

2. Calculate \( (\sqrt{73})^2 \):
\[
(\sqrt{73})^2 = 73
\]

Since \( \sqrt{73} \, \text{ft} \) is longer than \( 8 \, \text{ft} \), it will be treated as the hypotenuse \( c \):

Thus, using the Pythagorean theorem:
\[
8^2 + a^2 = (\sqrt{73})^2
\]

Substituting the values we have:
\[
64 + a^2 = 73
\]

To find \( a^2 \):
\[
a^2 = 73 - 64
\]
\[
a^2 = 9
\]

Taking the square root of both sides:
\[
a = \sqrt{9} = 3 \, \text{ft}
\]

So, the length of the unknown side \( a \) is:

**3 ft.**