Question

What is the length of the unknown side of the right triangle?
Top: 8 ft
Side: a
Bottom: v73 ft

Answer 1

In a right triangle, we can use the Pythagorean theorem to find the length of an unknown side. The theorem states that:

\[
a^2 + b^2 = c^2
\]

where:
- \( a \) and \( b \) are the lengths of the legs of the triangle,
- \( c \) is the length of the hypotenuse.

From your description, we have:
- One side (leg) is \( a \),
- The other leg is \( 8 \) ft,
- The hypotenuse is \( \sqrt{73} \) ft.

We can set this up using the Pythagorean theorem:

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

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

\[
a^2 + 64 = 73
\]

Now, isolate \( a^2 \):

\[
a^2 = 73 - 64
\]
\[
a^2 = 9
\]

Now, take the square root to find \( a \):

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

Thus, the length of the unknown side \( a \) is **3 feet**.